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  • Integrate: sin x cos x ( 2sin x +3cos x)

Integrate: sin x cos x ( 2sin x +3cos x)

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Solution: We have , 

                  I=int sin x cos x (2sin x +3cos x)dx

             \ \ Rightarrow I=2int sin^2x cos x dx+3int sin x cos ^2x dx

      Substitute           sin x=y  in the first integral  and  cos x=t in the second Integral

        We get ,

       Rightarrow    I= 2int y^2dy-3int t^2dt=frac23y^3-t^3+c

      \ \ Rightarrow I= frac23sin^3x-cos^3x+c.

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Deependra Verma

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