Integral of tan(x)*ln(cos(x))

Answers

Answer 1

Answer:

[tex]\int {tan(x)*ln(cos(x))} \, dx = -\frac{ln^2cos(x)}{2} + c[/tex]

Explanation:

Given

[tex]tan(x)*ln(cos(x))[/tex]

Required

Integrate

This is represented as:

[tex]\int {tan(x)*ln(cos(x))} \, dx[/tex]

Let

[tex]u =- ln(cos(x))[/tex]

So that:

[tex]\frac{du}{dx} = \frac{sin(x)}{cos(x)}[/tex]

Make dx the subject

[tex]dx = \frac{cos(x)}{sin(x)}du[/tex]

[tex]\int {tan(x)*ln(cos(x))} \, dx[/tex] becomes

[tex]\int {-u *tan(x)*\frac{cos(x)}{sin(x)}du[/tex]

Express tan x as sin x/ cos x

[tex]\int {-u *\frac{sin(x)}{cos(x)}*\frac{cos(x)}{sin(x)}du[/tex]

[tex]\int {-u du[/tex]

[tex]-\int {u du[/tex]

Apply power rule

[tex]-\frac{u^{1+1}}{1+1} + c[/tex]

[tex]-\frac{u^{2}}{2} + c[/tex]

Substitute [tex]u =- ln(cos(x))[/tex]

[tex]-\frac{ln^2cos(x)}{2} + c[/tex]

Hence:

[tex]\int {tan(x)*ln(cos(x))} \, dx = -\frac{ln^2cos(x)}{2} + c[/tex]


Related Questions

) Describe a change in ocean circulation that results from an El Niño event that is represented in the model

Answers

You should show the model and the thing you are exactly talking about

El Niño is a warmer phase of the ENSO that is the warming of the oceanic water that develops in the central-eastern Pacific. It is a cycle of the warm and sea surface temperature.

Warm surface water currents, warm water moves east not in the western direction. Coldwater creases off the coasts of South America. Nutrient-rich from the deep ocean is not brought up towards the surface. The surface water in the southern and eastern pacific oceans gets warmer.

Learn more about the hanged in ocean circulation that results from an El Niño event.

brainly.com/question/7543073.

Two type of microscopes used to view cells are optical and__ microscopes

options:

laser
Electron

Answers

Answer: Electron

Explanation:

Two type of microscopes that are used to view cells are optical and the electron microscopes.

The optical microscope, is also called the light microscope, and it uses visible light and lenses to magnify small objects and make them bigger. It is used in viewing cells as they appear big.

Electron microscope gives a high resolution images of specimens. The electron microscope is used in medicine to investigate tissues, cells, etc.

Sara and Greg built an electromagnet in science class. They wrapped 50 turns of copper wire around an iron nail and hooked the ends of the wire to a 1.5 volt battery. They picked up 15 paper clips with their electromagnet, but they want to make it stronger. What should they do?

Answers

Answer: C) Wrap more turns of wire around the nail.

Explanation:

One of the main determinants of the strength of a magnet is the number of rounds of wire around the magnet. This is because, the more wire there is, the more electricity will pass through and the more powerful the magnet will become.

They should therefore wrap more turns of wire around the nail so that more electricity can flow from the battery. This will make their magnet stronger and enable it to pick up more paper clips.

Please help!
What roles do globalization and interdependence play in economic development across regions?

Answers

Answer:

Globalization and interdependence have economic effects, like the increased competition between local and foreign businesses, investment of multinational companies in the developing world, employment opportunities in some regions, and unemployment in others.

What are the answers?

Answers

The answer to the question would be 15 and 10

Various impairments of the mind are commonly associated with old age. To what extent are these biological in origin? To what extent, social in origin?

Answers

Answer:

Timing and Course of Depression

Age of onset of major depression may have both clinical and etiological implications. Clinically, earlier age of onset is associated with a worse course of depression with greater chances of recurrence, chronicity, and impairment. Etiologically, first onset of depression at different ages (e.g., childhood, adolescent, adult, and older adult) may reflect somewhat different causal factors.

Many individuals may experience a single, major depressive episode following an acute stressor and recover with little implication for future vulnerability. However, most (50–80 percent) who have one significant episode will have recurrent episodes and intermittent subclinical symptoms, with the risk of recurrence progressively increasing with each episode of major depression.

Biological Factors

Genetic, neurological, hormonal, immunological, and neuroendocrinological mechanisms appear to play a role in the development of major depression, and many of these factors center around reactions to stressors and the processing of emotional information. Etiological processes may be modified by gender and developmental factors.

Environmental and Personal Vulnerabilities

Etiological models for depression are largely diathesis-stress models in which stressful experiences trigger depression in those who may be vulnerable due to biological and psychosocial characteristics and circumstances.

Environmental stressors associated with depression include acute life events, chronic stress, and childhood exposure to adversity. Personal vulnerabilities associated with depression include cognitive, interpersonal, and personality factors.

Biological, environmental, and personal vulnerabilities interact to contribute to the development of depression and also may be affected by depressive states in a bidirectional process.

Co-Occurring Disorders

Depression rarely occurs independent of other psychological disorders, including anxiety, substance abuse, behavioral, and personality disorders, as well as other medical illnesses. The presence of co-occurring psychological and medical disorders exacerbates the clinical and social consequences of depression, and makes it more challenging treating.

Resilience and Protective Factors

Certain biological, environmental, and personal factors have also been associated with the protection from or the overcoming of risk factors and adverse conditions related to the development of depression.

The purpose of this chapter is to review what is known or suspected about the causes of depression. Fundamentally, such depressive symptoms as sad mood, pessimism, and lethargy, are universal human experiences and are considered normal reactions to the struggles, disappointments, and losses of everyday life. However, for some individuals, the intensity and persistence of depressive symptoms are not typical, and a challenge for researchers has been to understand why some individuals experience marked and enduring depressive reactions and others do not. This chapter discusses some characteristics of individuals that may make them vulnerable, as well as the features of environments that are particularly likely to provoke depression. The chapter also emphasizes the interplay between persons and environments—the ways in which, for example, stressors may provoke depression but depression further influences social environments, often a vicious cycle that promotes chronic or recurrent depression. A further aspect of this bidirectional influence is the frequent co-occurrence of depression and other disorders, which may complicate its course and treatment. It is noted that some individuals are remarkably resilient in the face of adversity, and a further challenge to the field is to understand such processes.

The first topic to address is that not all depressions are alike; therefore, different etiological models and perspectives are likely to apply to different expressions of depressive disorder.

At Lakeview High School, students either walk to school or provide their own transportation. Suppose that those who walk have a mean commute time of 121212 minutes with a standard deviation of 555 minutes, while those who use some other form of travel have a mean and standard deviation of 161616 and 666 minutes, respectively. The principal takes an SRS of 505050 students who walk, and an independent SRS of 303030 students who use some other form of travel. The principle calculates the mean commute time for each sample, then looks at the difference (\text{Other}-\text{Walk})(Other−Walk)left parenthesis, start text, O, t, h, e, r, end text, minus, start text, W, a, l, k, end text, right parenthesis between the sample means.

Answers

Answer:

A

Explanation:

on khan academy

Which term is one for the widest diameter of a skeletal muscle?

Answers

Answer:

type IIb fibers

Explanation:

That's the answer mate.

In the lab experiement you are making solutions and need a precise graduation line in the neck of the flask. Which would
you choose?
A) filter
B) volumetric
C) Florance
D) Erlenmeyer
Please select the best answer from the choices provided
A
B
С
D

Answers

Answer:

B) volumetric

Explanation:

Explain ONE historical development after 1900 that reflects the
Soviet hanging order from Vladimir Lenin.

Answers

Answer:

In the 1920s an Indian tribe by the name of the American Indian Osage tribe moved to a land that luckily enough was rich in oil supply. Soon after these natives were all killed due to their newfound wealth just like the Soviet hanging order from Vladmir Lenin.

Explanation:

All cells are the same size

True
False

also if I give u brainlist’s can u give them back? (for answering this question)

Answers

Answer:

false

Explanation:

All cells are the same shape, but not all cells are the same size. Different cells can have both different sizes and different shapes.

have  a wonderful  day! :)

Pleaseeee help it’s for a Human Resources class

Answers

I would say systematic since the other ones don’t seem correct

6. Drivers with a BAL of .05 are about
times more likely to be
involved in a fatal collision than sober
drivers.

Answers

Answer:

5

Explanation:

Drivers with a BAL of .05 are about  5 times more likely to be

involved in a fatal collision than sober  drivers.

1. What are two things you can never eat for breakfast?

2. What is always coming but never arrives?

3. What gets wetter the more it dries?

4. What can be broken but never held?

5. What word is spelled incorrectly in every single dictionary?

6. What is it that lives if it is fed, and dies if you give it a drink?

7. What never asks a question but gets answered all the time?

8. What word would you use to describe a man who does not have all his fingers on one hand?

9. What goes up but never ever comes down?

10. What can one catch that is not thrown?

Answers

Answer:

1. lunch and dinner

2. tomorrow

3. a towel

4. promise

5. wrong

6. fire

7. doorbell

8. normal

9. age or hot air

Explanation:

do you think a democracy should be totally open or can it mantain secrecy​

Answers

Answer:

can be maintained secrecy

PLEASEEEE HELP it’s for a Human Resources class

Answers

Answer:

c

Explanation:

im smart

Which of the following will most likely result in an increase in deficit spending

Answers

What is which of the following we need the options lol

How do you use critical thinking skills in completing your coursework at Underwood University?

Answers

Answer:

Critical Thinking

Thinking comes naturally. You don’t have to make it happen—it just does. But you can make it happen in different ways. For example, you can think positively or negatively. You can think with “heart” and you can think with rational judgment. You can also think strategically and analytically, and mathematically and scientifically. These are a few of multiple ways in which the mind can process thought.

What are some forms of thinking you use? When do you use them, and why?

As a college student, you are tasked with engaging and expanding your thinking skills. One of the most important of these skills is critical thinking. Critical thinking is important because it relates to nearly all tasks, situations, topics, careers, environments, challenges, and opportunities. It’s a “domain-general” thinking skill—not a thinking skill that’s reserved for a one subject alone or restricted to a particular subject area.

Great leaders have highly attuned critical thinking skills, and you can, too. In fact, you probably have a lot of these skills already. Of all your thinking skills, critical thinking may have the greatest value.

What Is Critical Thinking?

Critical thinking is clear, reasonable, reflective thinking focused on deciding what to believe or do. It means asking probing questions like, “How do we know?” or “Is this true in every case or just in this instance?” It involves being skeptical and challenging assumptions, rather than simply memorizing facts or blindly accepting what you hear or read.

Imagine, for example, that you’re reading a history textbook. You wonder who wrote it and why, because you detect certain biases in the writing. You find that the author has a limited scope of research focused only on a particular group within a population. In this case, your critical thinking reveals that there are “other sides to the story.”

Who are critical thinkers, and what characteristics do they have in common? Critical thinkers are usually curious and reflective people. They like to explore and probe new areas and seek knowledge, clarification, and new solutions. They ask pertinent questions, evaluate statements and arguments, and they distinguish between facts and opinion. They are also willing to examine their own beliefs, possessing a manner of humility that allows them to admit lack of knowledge or understanding when needed. They are open to changing their mind. Perhaps most of all, they actively enjoy learning, and seeking new knowledge is a lifelong pursuit.

This may well be you!

No matter where you are on the road to being a critical thinker, you can always more fully develop and finely tune your skills. Doing so will help you develop more balanced arguments, express yourself clearly, read critically, and glean important information efficiently. Critical thinking skills will help you in any profession or any circumstance of life, from science to art to business to teaching. With critical thinking, you become a clearer thinker and problem solver.

Critical Thinking IS Critical Thinking is NOT

Skepticism Memorizing

Examining assumptions Group thinking

Challenging reasoning Blind acceptance of authority

Uncovering biases

The following video, from Lawrence Bland, presents the major concepts and benefits of critical thinking.

what are 5 questions of trust in the lifespan development

Answers

Answer:

Im sorry so very hard

Thank you bye

at what price is there an excess supply of 1000?

Answers

I would say about 153 or in the 150’s. I can’t pinpoint the answer since the picture is a little bit blurry.

In the context of the second paragraph, the author describes dinosaurs as "the most charismatic characters in the fossil record" primarily to

A) explain why only one of several mass extinctions has received coverage in the popular media

B) argue that the general public’s fascination with only one of several mass extinctions is scientifically scientifically justified

C) Account for the relative lack of research on extinct lifeforms other than dinosaurs

D) defend the great importance paleontologist attached to the end crustaceous mass extension

E) clarify the context in which researchers first began to understand the causes of mass extinction

Answers

Answer:

A. explain why only one of several mass extinctions has received coverage in the popular media

Explanation:

i"ll update afterwards to see :)

Answer:

A) explain why only one of several mass extinctions has received coverage in the popular media

Explanation:

The author acknowledges that there are reasons why the four mass extinctions preceding the End-Cretaceous “are invisible, for the most part, in the public imagination.” He then goes on to explain these reasons by citing the dinosaurs, which he defines with a modifying phrase (“the most charismatic characters in the fossil record”). It is this charisma that has made the End-Cretaceous extinction famous and allowed the dinosaurs to “hog most of the popular press spared for paleontology.” Thus the modifying phrase helps to specify or limit the reasons for the dinosaurs’ high media profile. In doing so, it advances the author’s larger argument by explaining why attention to the causes of mass extinction has been given only to the cause of the End-Cretaceous extinction (asteroids) rather than to the changes in climate and geology that were likely responsible for other mass extinctions.

Give an example of developmental psychology when the individual is in college

Answers

The correct answer to this open question is the following.

An example of developmental psychology when the individual is in college would be this.

Personality development is my example of how people change when they enter college.

Let's have in mind that developmental psychology is the field of psychology that studies the way people grow and change during life.

Psychologists not only focus on physical and evident changes from high school to college, but they focus on the mental, emotional, and social changes.

When entering college, the student aspires to be respected and attract a different kind of people. Not only on the emotional level to have a relationship, but on the influence level, trying to be recognized above the others.

That is why in college, students try to be more mature, appear more intellectually interesting, and want to get to a place of recognition and admiration among a fierce competition of personalities.

PLEASE HELP NEED ANSWER FAST

Answers

i would say A
A. the benefit of a diverse range of experiences
Yes A definitely seems like the most reasonable answer here

Please helppp it’s for a human resource class

Answers

Answer:

try A, if thats wrong then it's deffinently  D

Explanation:

The diagram shows the length and width of a cell phone, and the length of a larger
version of the same brand of cell phone.
2.6 in.
5.4 in.
6.21 in.
The lengths and widths of the two cell phones are proportional. What is the width,
in inches, of the larger version of the cell phone?

Answers

Answer:

The width of the bigger phone is 2.99 in

Explanation:

Given

[tex]W_1 = 2.6in[/tex]

[tex]L_1 = 5.4in[/tex]

[tex]L_2 = 6.21in[/tex]

See attachment for the measure of cell phones

Required

Determine the width of the bigger version (L2)

To do this, we make use of the following equivalent ratios.

[tex]L_1 : W_1 = L_2 : W_2[/tex]

This gives:

[tex]5.4\ in : 2.6\ in : 6.21\ in : W_2[/tex]

Express as fractions

[tex]\frac{5.4\ in}{2.6\ in} = \frac{6.21\ in}{W_2}[/tex]

[tex]\frac{5.4}{2.6} = \frac{6.21\ in}{W_2}[/tex]

Make W2 the subject

[tex]W_2 = \frac{6.21 * 2.6\ in}{5.4}[/tex]

[tex]W_2 = \frac{16.146\ in}{5.4}[/tex]

[tex]W_2 = 2.99\ in[/tex]

Match the role with the actions taken by players in that role,
Worker
?
Uses goods and services,
Producer
?
Provides goods and
services,
Consumer
?
Creates goods and
services,

Answers

Answer:

Consumer = Uses goods and services

Worker = Creates good and services

Producers = Provides goods and services

Explanation:

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Using what you have learned about development, give examples from your life (or
the lives of people you know) of physical, cognitive, psychosocial, and moral
development (give an example for each).

Answers

Answer:

sowhenthesuncomesoutiusesomepunstoletmyselfshoutandevenwhenyourmomisindoubtireassureherthatshesontherightroute

Explanation:

Answer:

Physical development is when I started growing and when I went through a growth spurt in middle school. Cognitive is going to school and learning things, especially about things I enjoy. Psychosocial is about learning how to make friends and growing relationships with people like my closest friends. Moral development from when I began learning about issues around the world and began doing volunteer work to help others.

Explanation:

Got 100% on the assignment :) Hope this helps!

Could you tell me something baout Odoo platform for events

Answers

Answer:

Odoo is a suite of open source business apps that cover all your company needs: CRM, eCommerce, accounting, inventory, point of sale, project management, etc.

Kevin lives with his parents and is

Answers

? I can help can u continue?

3. When the government finances a deficit, the government will:
A. Lower taxes.
B. Increase spending.
C. Reduce interest rates
D. Borrow money
E. Increase transfer payment.

Answers

Answer:

D. Borrow Money

hope that helps you good luck

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