Question: Prove that cot u du = ln|sin u|+ C.

Prove that ∫ cot u du = ln|sin u|+ C.

Step by Step Solution

★★★★★

3.45 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We can start the proof by using integration by parts Let fu lnsin u gu co... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

2) a) For the circuit below, what is the charge on each of the capacitors once steady state conditions are reached? b) What is the reading on the ammeter after 3 ms? A 2000 3000 120 V +10 2 uf 1H 3...

Q:

find one example from the news media that you can link --either videos, podcasts, articles, reports, television broadcasts, etc.--that exhibit what you take to be a valid and sound deductive argument.

Q:

\fTABLE OF INTEGRALS Basic Forms 1. Jude = w - v du 11. csc u cot u du = - escu + C n+ + C. nx-1 12. tan u du = In | sec u | + C 3. - = In Ju+ c 13. cot u du = In | sin a | + C A. ( e" du = e" + C...

Q:

Please answer all questions. Neatly please R.K. Sahi (10 points) Fill in the blanks. (a) The first rule that we would use to find the derivative of f(x) = xIn(Vx + 1) is Hint: Chain Rule, Product...

Q:

Evaluate the integrals of the following: 1. f cos3 xdx 2. f cos x dx 3. J cos* 3x dx sin2 3x 4. f sin2 5x tan 5x dx da 5. J 6 w-2-902 x*dx 6. x2+1 7. S tan x 8. f cot5 2ydy 9 .S sin' tat cost 10f sin...

Q:

Suppose that A : {61:1, . . . , 63-}, B : {31, . . . ,gj}, and C : {51, . . . , 5k} are all subsets of an n-dimensional vector space V over F. Suppose further that Span(A) : Span(B). Prove that...

Q:

3. Prove that pet U = P ( a, b , c, d) ER / a + 2 1 + C + 3d = a - 4 + 40 + 2d= 04 foams a states standard rectoria space R and calculate the dimension of it. Also give an example of twoo to...

Q:

MATH260Week 6 Lab Name: Antiderivatives According to the first part of the fundamental theorem of calculus, the antiderivative reverses the derivative. If f(x) is a derivative, F(x) is the...

Q:

Cette mission est trs urgente ! Soyez aussi prcis que possible en expliquant chaque rponse. Chapitre 1 1. La comptabilit de gestion et la comptabilit financire diffrent de la manire suivante: A.La...

Q:

7/4/23, 11:16 PM Homework 8.7-Anh Nguyen Use a table of integrals to determine tv7t+ 19 at. Click here to view page 1 of the integral table. " Click here to view page 2 of the integral table. 14...

Q:

Compare that to the same issues for a new company. Provide examples of a service or product that has a 'mature' or older option and an innovative or new technology, both of which are still available...

Q:

A cost-benefit analysis of a new irrigation project indicates that the net benefits of the project in each of the first four years will be -$2 million. That is, Bi - Ci = -2 million for i = 1, 2, 3,...

Q:

Do you think Rick will ever get it together? What are the real causes of his frustration? Why isnt Arturo having the same kinds of problems?

Q:

6.39. An article in Quality and Reliability Engineering International (2010, Vol. 26, pp. 223233) presents a 25 factorial design. The experiment is shown in Table P6.12. (a) Analyze the data from...

Q:

In Exercises use integration to find a general solution of the differential equation. dy dx =6x2

Q:

In Exercises find the orthogonal trajectories of the family. Use a graphing utility to graph several members of each family. x - 2y = C

Q:

In Exercises complete the table for a savings account in which interest is compounded continuously. Initial Investment $750 Annual Rate Time to Double 73 yr Amount After 10 Years

Q:

If two options, one American and one European, have the same exercise price X and time to expiration T, it is expected that" The price of the American option is greater than or equal to the European...

Q:

A computer system purchased by Jones Company cost $45,900. Using the MACRS method, calculate the accumulated depreciation at the end of year 3. (Round all dollar amounts to the nearest cent)

Q:

Barnette Inc.'s free cash flows are expected to be unstable during the next few years while the company undergoes restructuring. However, FCF is expected to be $50 million in Year 5, i.e., FCF at t =...