Chapter 8, Problem 31RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Using Trigonometric Substitution In Exercises 29–34, use trigonometric substitution to find or evaluate the integral. ∫ x 3 4 + x 2 d x

To determine

To calculate: The value of the integral x34+x2dx

Explanation

Given:

The integral âˆ«x34+x2dx

Formula used:

If the function, u=g(x) has a continuous derivative on the closed interval [a,b] and f is continuous on the range of g, then

âˆ«abf(g(x))gâ€²(x)dx=âˆ«g(a)g(b)f(u)du

For the integral xn

âˆ«xndx=xn+1n+1

Calculation:

Let x=2tanu,dx=2sec2udu

4+x2=4sec2ux2+42=secu

The given integral is solved as,

âˆ«x34+x2dx=âˆ«8tan3u2secu(2sec2udu)

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