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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
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Integrating Inverses of FunctionsIntegration by parts

Chapter 8, Problem 73E

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QUESTION:

Problem 73E

Integrating Inverses of Functions

Integration by parts leads to a rule for integrating inverses that usually gives good results:

The idea is to take the most complicated part of the integral, in this f-1(x) case and simplify it first. For the integral of ln x, we get

For the integral of cos-1 x we get

Use the formula

to evaluate the integrals. Express your answers in terms of x.

Questions & Answers

QUESTION:

Problem 73E

Integrating Inverses of Functions

Integration by parts leads to a rule for integrating inverses that usually gives good results:

The idea is to take the most complicated part of the integral, in this f-1(x) case and simplify it first. For the integral of ln x, we get

For the integral of cos-1 x we get

Use the formula

to evaluate the integrals. Express your answers in terms of x.

ANSWER:

Solution:

Step 1 of 3:

In this problem, we need to evaluate the integral.

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