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Question

ex sin2 x dx

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Solution

Let I= exsin2 x dx= ex 1-cos 2x2dx=12 ex dx-12 ex cos 2x dx=ex2-12 excos 2x dx .....1Let I1= excos 2xdxConsidering cos 2x as first function and ex as second functionI1=cos 2xex--2 sin 2xex dxI1=cos 2xex+2 sin 2xex dxI1=cos 2xex+2sin 2xex- 2 cos 2xex dxI1=cos 2xex+2 sin 2xex-4I15I1=ex cos 2x+2 sin 2xI1=ex5cos 2x+2 sin 2x+C .....2From 1 & 2I=ex2-ex10cos 2x+2 sin 2x+C

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