10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral.

∫ sin 3 x cos 2 x d x

To determine

To calculate: The value of indefinite integral given as, ∫sin3xcos2xdx.

The expression is ∫sin3xcos2xdx.

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=∫sin3xcos2xdx

Simplify it to a form where the power rule can be used,

I=∫sin3xcos2xdx=∫sin2xcos2xsinxdx=∫(1−cos2x)cos2xsinxdx=∫cos2xsinxdx−∫cos4xsinxdx

Check out a sample textbook solution.

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Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral. ∫ sin 3 x cos 2 x d x

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Calculus Calculus 10th Edition

Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral.

∫ sin 3 x cos 2 x d x