Question: Use integration by parts to prove the reduction formula. a. (ln x)n dx = x(ln x)n - n (ln x)n-1 dx b.

Use integration by parts to prove the reduction formula.
a. ∫ (ln x)n dx = x(ln x)n - n ∫ (ln x)n-1 dx
b. ∫ tannx dx = = (tann-1 x)/(n - 1) - ∫ tann-2 x dx (n ≠ 1)

Step by Step Solution

★★★★★

3.32 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let u ln x n dv dx du n1nx n1 dx x v x By Equation 2 Inx n dx x ln x n nx lnx n1 dx x x lnx n n ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

786-C-I (682).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Use integration by parts to show that Г(r) = (r 1) Г(r 1).

Use integration by parts to show that, for all x > 0, sin ! dt

Use integration by parts to show that () = ( 1) ( 1) for > 1.

In Exercises use integration by parts to verify the reduction formula. Ss sec" x dx = 1 n- 1 sec 2 x tan x + n n 2 1 - sec-2 x dx

In Exercises use integration by parts to verify the reduction formula. S cos" x dx = "="f n cos"- x sin x n + n cos"-2 x dx

In Exercises use integration by parts to verify the reduction formula. Ja cosm x sin" x dx = cosm+1 x sinn-1 x m+n S 1 n m + n + cosm x sinn-2 x dx

Use integration by parts to derive the following formula x " . In / x / dx = x" + In x n+1 + Cin -1 (n + 1)- Find uv. uv = Integrate vdu vdu = After finding uv, integrating vdu, and subtracting vdu...

Use integration by parts to obtain a reduction formula for positive integers n: Use this reduction formula to evaluate sin 6 x dx. sin" x dx = -sin" x cos x + (n 1) | sin"-2 x cos? x dx. -1 sin"-'x...

1. Use integration by parts to prove the following reduction formula. (14 pts) -1 n - 2 csch x dx = csch-2 x cotx + csch-2 x dx n - 1 n - 1

Section 8.3 Reading Assignment: Trigonometric Integrals Instructions. Read through this assignment and complete the three exercises below by reading the appropriate passages of the textbook. This...

Week 1 2 3 4 5 6 LC% 30% 60% 70% 80% 90% 100% We have a new team with this learning curve and a labor cost of $ 1.3 per unit. If the capacity is 16,457 units per week, how much would be the labor...

Thinking of a product that is moving toward convergence, how will convergence influence the marketing managers job?

Bills referred to standing committees by the party leadership have greater success in being reported favorably out of committee.

Colorblind Although some women are colorblind, this condition is found primarily in men. Why is it wrong to say theres a strong correlation between Sex and Colorblindness?

(a) If f (x) e x cos x, find f'(x) and f''(x). (b) Check to see that your answers to part (a) are reasonable by graphing f , f', and f''.

Differentiate the function. A + Bz + Cz F(2) : z2

8.3 The accountant of your business has recently been taken ill through overwork. In his absence his assistant has prepared some calculations of the profitability of a project, which are to be...

Below, you will find Treasury Bond quotes. To calculate the number of years until maturity, assume that it is currently May 2013. Rate maturity (mo/yr) Bid Asked Chg Ask Yld ?? May 19 103.5592...

Given the following term structure, what is the forward rate of a 3-year treasury bond issued 1 year from now? What is the forward rate of a 2-yeat treasury bond issued 3 year from nowipiease answer...