Q.95. Integration.

Question 95.
Find ∫ x^2 [(1-x) / (1+x)] dx.

Answer 95.
x^2 [(1-x) / (1+x)]
= - (x^3 - x^2) / (1 + x)
= - (x^3 + x^2 - 2x^2 - 2x + 2x + 2 - 2) / (x + 1)
= - [ x^2(x + 1) - 2x(x + 1) + 2(x + 1) - 2] / (x + 1)
= - x^2 + 2x - 2 + 2 /(x + 1)

=> ∫ x^2 [(1-x) / (1+x)] dx
= ∫ [ - x^2 + 2x - 2 + 2 /(x + 1) ] dx
= - (x^3) / 3 + x^2 - 2x + 2 ln l x + 1 l + c

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