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Question

The integral 10tan1(2x11+xx2)dx simlifies to a value:

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Solution

10tan1(2x11+xx2)dx
=10tan1(x+x11x(x1))dx
10(tan1x+tan1(x1))dx
10tan1xdx+10tan1(x1)dx
Applying a0f(x)dx=a0f(ax)dx in the first integral
=10tan1(1x)dx+10tan1(x1)dx
=10tan1(1x)dx10tan1(1x)dx=0

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