integrate (x2 + x)/(ex+x+1)2 w.r.t x

Hi Suchita,

take e^x common from denominator,

then you have.............  e^-xxe^-x(x+1)/(1+xe^-x+e^-x)²

Make the substitution, 1/(1+xe^-x+e^-x) = t, and you will get

xe^-x/(1+xe^-x+e^-x)²dx = dt, and xe^-x+e^-x = (1/t)-1.

So after this substitution, you have Integral of [(1/t)-1] = lnt - t + Const. And substitute for t from above.

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).

Approved