   Chapter 8.3, Problem 3E

Chapter
Section
Textbook Problem

Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral. ∫ cos 5 x   sin x   d x

To determine

To calculate: The value of indefinite integral given as, cos5xsinxdx.

Explanation

Given:

The required expression is cos5xsinxdx.

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:

Finding an indefinite integral of a function means integrating the function without any limits. If limits are applied, they can be done so directly by putting the limits in the integrated expression.

Consider the integral to be I,

I=cos5xsinxdx

For the integral, involve powers of sine and cosine,

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

du=sinxdx

Substitute the value, cosx=u

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