integrate (5x⁴+4x⁵)/(x⁵+x+1)² w.r.t x

Hi Suchita,

The integral can be written as

{x⁴(5+4x)}/{x¹⁰(1+1/x⁴+1/x⁵)²}

Now make the substitution 1+1/x⁴+1/x⁵ = t

and you will get (5+4x)/x⁶ dx = dt.

And the integral reduces to ∫1/t² dt.

And after that it is simple and direct integration, and that solves the problem.

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).