1.

Integrate the following functions x^3/sqrt(1-x^8)

Answer»

SOLUTION :`int x^3/sqrt(1-x^8) DX = int x^3/sqrt(1-(x^4)^2) dx`.
put `t = x^4`. Then `DT = 4x^3 dx`
therefore REQUIRED INTEGRAL
=`int 1/sqrt(1-t^2) 1/4 dt = 1/4 sin^-1 t+c`
=`1/4 sin^-1 x^4 +c`


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