∫x⁵dx/√(1-x²)

Hi Suhas,

 

Substitute 1-x^2 = t^2, so that xdx = -tdt

And x^4 = (1-t^2)^2.

 

Integral will be ∫(1-t^2)^2dt.

This is directly integrable, once you expand it.

 

Hope it helps.

 

Best Regards,

Ashwin (IIT MadraS).

1-x^2/x^5 = -x^3 -x + x/1-x^2 then easily interegrate all these so ans - -X^4/4-X^2/2 + LOG(1-X^2)/2 = CONST.