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Question

xcos3(x2)sin(x2)dx is equal to

A
cos4(x2)sin(x2)16+C
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B
cos(x2)16+C
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C
cos4(x2)8+C
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D
cos3(x4)8+C
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Solution

The correct option is C cos4(x2)8+C
xcos3(x2)sin(x2)dx
Let x2=t2x dx=dt
=12cos3(t)sin(t) dt
Let cost=zsint dt=dz
=12z3dx=z48+c1=cos4(x2)8+C

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