   Chapter 8.7, Problem 53E

Chapter
Section
Textbook Problem

Verifying a Formula In Exercises 49-54, verify the integration formula. ∫ arctan u   d u = u arctan u − ln 1 + u 2 + C

To determine

To prove: The formula (arctanu)du=uarctanuln1+u2+C.

Explanation

Given:

(arctanu)du=uarctanuln1+u2+C

Formula used:

The formula used is integration by parts, u and v are two terms:

uv=uv(v)u

1xdx=lnx

xndx=xn+1n+1

1dx=x+c

Proof:

Let w=arctanu,v=1,

(arctanu)du=arctanu(

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