   Chapter 8.5, Problem 35E ### 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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# Integration by Parts In Exercises 33-38, use integration by parts to find the indefinite integral. ∫ 6 x   sec 2   x   d x

To determine

To calculate: The integral of 6xsec2xdx.

Explanation

Given Information:

The provided integral is 6xsec2xdx.

Formula used:

Write the formula used in integration by parts method.

pqdx=pqdxp(qdx)dx

Here, p=p(x) and q=q(x)

Write the formula of integral of sec2u.

sec2udu=tanu+C

Write the formula of integral of tanu.

tanudu=ln|cosu|+C

Write the formula for derivative of un.

ddxun=nun1

The provided integral is,

6xsec2xdx

Use the formula of integration by parts to find integral of above expression.

6xsec2xdx=6xsec2xdxddx6x(sec2xdx)dx=6xsec2xdx6(sec2xdx)dx

Here, p=6x and q=sec2x

Let u=x

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