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Question

Evaluate x2sinx dx

A
x2cosx+2(xsinx+cosx)
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B
x2cosx2(xsinx+cosx)
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C
x2cosx+(2xsinx+cosx)
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D
x2cosx(2xsinxcosx)
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Solution

The correct option is A x2cosx+2(xsinx+cosx)
Given, x2sinx dx
Using Integration by parts method we have,
x2sinx dx=x2sinx dxdx2dx(sinx dx) dx
x2cosx+2xcosx dx
x2cosx+2[xcosx dxdxdx(cosx dx)dx]
x2cosx+2(xsinxsinx dx)
x2cosx+2(xsinx+cosx)

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