How to solve \(\displaystyle\int{{\sin}^{{3}}{\left({x}\right)}}{{\cos}^{{2}}{\left({x}\right)}}{\left.{d}{x}\right.}\) with integration by

blestimd4pz

blestimd4pz

Answered question

2022-03-29

How to solve sin3(x)cos2(x)dx with integration by parts?

Answer & Explanation

microsgopx6z7

microsgopx6z7

Beginner2022-03-30Added 14 answers

sin3xcos2xdx=sin2xcos2xd(cosx)=
=(1cos2x)cos2xd(cosx)=cos4xcos2xd(cosx)=
=cos5x5cos3x3+C
lernarfnincln6g

lernarfnincln6g

Beginner2022-03-31Added 14 answers

split your integral and write
sin(x)3(1sin(x)2)=sin(x)3sin(x)5
furthere use that
sin(x)3=14(3sin(x)sin(3x))
and
sin(x)5=116(10sin(x)5sin(3x)+sin(5x))

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