Answer
$\ln|x^{4}+3x|$ + C
Work Step by Step
$\int\frac{4x^{3}+3}{x^{4}+3x} dx $
Let $u =x^{4}+3x$
$\frac{du}{dx}$ = $4x^{3}+3$
$\frac{du}{4x^{3}+3}$ = $dx$
Substitute $u$ and $dx$ into the original equation
$\int\frac{4x^{3}+3}{u}\frac{du}{4x^{3}+3}$
= $\int\frac{4x^{3}+3}{4x^{3}+3}\frac{1}{u} du$
= $\int\frac{1}{u} du$
= $\ln|u|$ + C
Since $u =x^{4}+3x$, substituting it back will give you
$\ln|x^{4}+3x|$ + C
