   Chapter 8.5, Problem 38E ### 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. ∫ θ 7 sec θ 7 tan θ 7 d θ

To determine

To calculate: The integral of θ7secθ7tanθ7dθ.

Explanation

Given Information:

The provided integral is θ7secθ7tanθ7dθ.

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 secutanu.

secutanudu=secu+C

Write the formula of integral of secu.

secudu=ln|secu+tanu|+C

Write the formula for derivative of un.

ddxun=nun1

The provided integral is,

θ7secθ7tanθ7dθ

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

θ7secθ7tanθ7dθ=θ7secθ7tanθ7dθddθ(θ7)(secθ7tanθ7dθ)dθ=θ7secθ7tanθ7dθ17(secθ7tanθ7dθ)dθ

Here, p=θ7 and q=secθ7tanθ7

Multiply and divide by 7.

θ7secθ7tanθ7dθ=7θ7(secθ7tanθ7)17dθI717((secθ7tanθ7)17dθ)dθII

Again, multiply and divide by 7 in second part.

θ7secθ7tanθ7dθ=θ(secθ7tanθ7)17dθ4917((secθ7tanθ7)17dθ)17dθ

Consider u=θ7

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