   Chapter 7.5, Problem 72E

Chapter
Section
Textbook Problem

# 7.5 EXERCISESEvaluate the integral. ∫ ln ( x + 1 ) x 2 d x

To determine

To find:

ln(x+1)x2dx

Explanation

Formula used: 1. Integration by parts

Calculations: The given integral I can be simplified as

I=ln(1+x)×1x2dx

This may be solved using integration by parts.

Let u=ln1+x, du=11+x

also dv=1x2dx, v=-1x

The integral I can now be written as

I=vu -vdu=-1x×ln1+x--1x×11+xdx=-ln1+xx+1x(1+x)dx

To solve the integral on RHS use partial fractions

fx=

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