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Question

sin5x2sinx2dx is equal to:
(where c is a constant of integration.)

A
x+2sinx+sin2x+c
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B
x+2sinx+2sin2x+c
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C
2x+sinx+sin2x+c
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D
2x+sinx+2sin2x+c
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Solution

The correct option is A x+2sinx+sin2x+c
I=sin5x2sinx2dx
=2sin5x2cosx2sinxdx
=sin3x+sin2xsinxdx
=(3sinx4sin3x)+2sinxcosxsinxdx
=(34sin2x+2cosx)dx
=(32(1cos2x)+2cosx)dx
=(32+2cos2x+2cosx)dx
=(1+2cos2x+2cosx)dx
=x+sin2x+2sinx+c

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