intergal by subsitution?

Question

intergal of (x^3)/(squre root of 1+x^3) dx

Answer 1

So sorry, but you can't do this by substitution.
It can be reduced to solving an elliptic integral
of the first kind. For a solution see integrals.wolfram.com .

Answer 2

I believe this can be solved like this for ex:
(u*v) dt = u * dv + v * du
so first allow u = x^3
v = (1+x^3)^-1 notice the -1 exponent placing it in the denominator
now do the above substitution so
[x^3]*[(-1*(1+x^3)^-2)*(3x^2)] + [(1+x^3)^-1]*[3x^2]
I'll let you simplify

Answer 3

This ain't subsitution
this is arctan stuff
The answer will be something like arctan(x^(3/2))