   Chapter 8.5, Problem 11E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integrating a Trigonometric Function In Exercises 1–32, find the indefinite integral. See Examples 1, 2, 3, 4, 5, and 8. ∫ tan 3   x   sec 2   x   d x

To determine

To calculate: The integral of tan3xsec2xdx.

Explanation

Given Information:

The provided integral is tan3xsec2xdx.

Formula used:

Write the formula of integral of un.

undu=un+1n+1+C

Write the formula for derivative of tanu.

ddx[tanu]=sec2ududx

Write the formula for derivative of xn.

ddxxn=nxn1

Calculation:

Consider u=tanx.

Differentiate the above considered function.

du=sec2xdx

The provided integral is,

tan3xsec2xdx

Rewrite.

tan3xsec2xdx=(tanx)3sec2xdx

Substitute u for tanx and du for sec2xdx

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