   Chapter 8, Problem 23RE

Chapter
Section
Textbook Problem

Finding a Trigonometric Integral In Exercises 17–26, find the trigonometric integral. ∫ x tan 4 x 2   d x

To determine

To calculate: The value of the integral xtan4x2dx

Explanation

Given:

The integral xtan4x2dx

Formula used:

If the function, u=g(x) has a continuous derivative on the closed interval [a,b] and f is continuous on the range of g, then

abf(g(x))g(x)dx=g(a)g(b)f(u)du

For the integral xn

xndx=xn+1n+1

Calculation:

The integral xtan4x2dx can be solved by taking sec2xdx=tanx

Also, here u=x2,du=2xdx

xtan4x2dx=12tan4ud

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