What is the integral of #sin^5 (x) * cos^3 (x)#?

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Answer 1 · 2016-06-02T19:24:00

#int sin^5 x*cos ^3 x d x=1/6sin^6 x-1/8 sin^8 x+C#

#int sin^5 x*cos ^3 x d x=?#

#int sin^5 x* cos^2x *cos x d x#

#cos^2 x=1-sin^2 x#

#int sin^5 x(1-sin^2 x) cos x d x#

#int (sin^5x-sin^7x)cos x d x#

#sin x=u" ; " cos x d x=d u#

#int (u^5-u^7)d u#

#int sin^5 x*cos ^3 x d x=1/6 u^6-1/8 u^8 +C#

#int sin^5 x*cos ^3 x d x=1/6sin^6 x-1/8 sin^8 x+C#