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Question

xsin2xdx

A
x24cos2x3+18sin2x+c
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B
x24xsin2x418cos2x+c
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C
x24+xsin2x4+18cos2x+c
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D
x24cos2x3+18cos2x+c
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Solution

The correct option is B x24xsin2x418cos2x+c
x sin2x dx.
=x sin2x. dx (sin2x.dx)dx
cos 2x=12 sin2x
2 sin2x=1cos 2x2
x (1cos 2x2)dx((1cos 2x2).dx)dx.
=x2[x 1/2sin 2x][x2 1/2sin 2x]dx
=x22x4sin 2x[x24+14cos 2x]
=x24x sin 2x418cos 2x+c

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