   Chapter 7.3, Problem 17E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x x 2 − 7   d x

To determine

To evaluate: The given integral xx27dx.

Explanation

Integration involving terms of the form x2a2 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, xx27dx

Calculation:

Use the substitution t=x27 to simplify the integral. The derivative of t will be dt=2xdx, so the integral will be:

xx2

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