   Chapter 8.1, Problem 74E

Chapter
Section
Textbook Problem

# Choosing a Formula In Exercises 73–76, state the integration formula you would use to perform the integration. Explain why you chose that formula. Do not integrate. ∫ x sec ( x 2 + 1 ) tan ( x 2 + 1 ) d x

To determine

The integration formula used to find the integral of xsex(x2+1)tan(x2+1)dx.

Explanation

Given:

The provided integral is xsex(x2+1)tan(x2+1)dx.

Let the integral I=xsex(x2+1)tan(x2+1)dx.

To solve the integral, first substitute sec(x2+1)=t then differentiate it with respect to t,

(2x)sec(x2+1)tan(x2+1)dx=dt

Then, the provided integral reduced to;

I=12

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