   Chapter 7.3, Problem 20E

Chapter
Section
Textbook Problem

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

To determine

To evaluate: The given integral x1+x2dx.

Explanation

Integration involving terms of the form a2+x2 can be simplified by using the trigonometric substitution x=asecθ. However, at times a simple algebraic substitution can also simplify the integral.

Formula used:

The derivative of xn is nxn1dx.

Given:

The integral, x1+x2dx

Calculation:

Use the substitution t=1+x2 to simplify the integral. The derivative of t will be dt=2xdx, so the integral will be:

x1+x2

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