   Chapter 8.3, Problem 4E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral. ∫ sin 3 3 x   d x

To determine

To calculate: The value of indefinite integral given as, sin33xdx.

Explanation

Given:

The expression, sin33xdx.

Formula used:

Integration of xn is given as,

xndx=xn+1n+1+C

Derivative of cosx with respect to x is given as,

ddx(cosx)=sinx

Calculation:

Consider the integral to be I,

I=sin33xdx

Simplify it to a form, such that power rule can be used,

I=sin33xdx=(sin23x)sin3xdx=(1cos23x)sin3xdx=sin3xdxcos23xsin3xdx

To solve an integral which involves the powers of sine and cosine,

Put, u=cos3x and differentiate both side with respect to x as,

du=3sin

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