   Chapter 7.5, Problem 76E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x 2 x 2 + 1 d x

To determine

To find:

x2dxx2+1

Explanation

Formula used:secx dx=lnsecx+tanx Reduction formula for secx

secnx=secn-1xsinxn-1+n-2n-1secn-2x

Calculations: Denote the given integral by I, then

I=x2dxx2+1

Let us do the following trigonometric substitution

Let x=tanu, dx=sec2u du and x2+1 = sec u

Thus

I=tan2u sec2u sec udu= tan2u sec u du

Simplifying using tan2u+1=sec2u  we have I=tan2u sec2u sec u

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