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Question

The value of [π402(1+x) ln (1+x)sinx+cosx2(1+x)cos3xdx] is (where [.] denotes the greatest integer function)

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Solution

I=π40(2 ln (1+x)sinx cosx+cos2x1+x2 cos4x) dxπ4012d(ln (1+x)cos2x)=12[ln (1+x)cos2x]π40=ln (1+π4)
So, [I] = 0

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