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Integrate the functions sin^3xcos^3x...

Integrate the functions `sin^3xcos^3x`

Text Solution

Verified by Experts

Given` ∫​sin^3xcos^3xdx`
=`1/8*∫​(2sinxcosx)^3dx`
=`1/8*∫​sin^((3)*2xdx`
putting 2x=t we get dx=2dt​
=`1/16*​∫​sin^(3)tdt`
=`1/16​∫​(3sint−sin3t​)/4 dt`
=`1/64*[−3cost+cos(3t)/3​]+c`
=`1/64[−3cos2x+cos(6x)/3​]+c`
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