Question

What is the integration of x²/1-x² w.r.t x​

Answer 1

Answer:

Step-by-step explanation:

∫ x^2/(1 -x^2) dx

=∫ (1-(1-x^2)) /1-x^2 dx

=∫ 1/(1-x^2) dx - ∫ (1-x^2) /(1-x^2) dx

For the first integration, put x= cosz, then dx =sinz dz

Now,

=∫ (sinz) /(1- cos^2z) dz - ∫dx

=∫ sinz/sin^2z dz -∫ dx

=∫ cosecz dz - ∫ dx

=(1/2) ln((cosz-1) /(cosz+1)) - x +c

=(1/2) ln((x-1) /(x+1)) -x+c [ where c is arbitrary constant]