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## Homework Statement

Take the integral of the following:

1. ln(2x+1)

2. arctan4x

3. e

^{cosx}sin2x evaluated from 0 to pi

## The Attempt at a Solution

1. took the derivative of ln(2x+1) and integrated dx. my solution was:

xln(2x +1) + x + [(2x + 1)

^{-2}]/2 + C

The books answer was:

(1/2)(2x + 1)ln(2x + 1) - x + C

2. took the derivative of arctan4x and the integrated dx. My solution was:

xarctan4x - (1+ x

^{2})

^{-2}+ C

The books answer was:

xarctan 4x - (1/8)ln(1 + 16x

^{2}) + C

3. I derived sin2x and integrated e

^{cosx}but I got something more complex than what I started with.