int (4x^3 + 3)/(x^4 + 3x) dx Find the indefinite integral.

int (4x^3+3)/(x^4+3x)dx
To solve, apply u-substitution method. So let:
u= x^4+3x
Then, differentiate it.
du=(4x^3+3)dx
Plug-in them to the integral. 
int (4x^3+3)/(x^4+3x)dx
= int 1/(x^4+3x)* (4x^3+3)dx
=int1/udu
Then, apply the integral formula  int 1/xdx = ln|x| + C .
= ln|u| + C
And, substitute back  u=x^4+3x .
=ln |x^4+3x|+C
 
Therefore,  int (4x^3+3)/(x^4+3x)dx = ln|x^4+3x|+C .