hey guys, a little confused on the order of this one. any step by step help is appreciated.
find the antiderivative:
$\displaystyle
f(x) = (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}$
Use the substitution rule: let $\displaystyle z := x^3+3x+2$. It follows that $\displaystyle dz = 3x^2+3=3(x^2+1)\,dx$, thus you have that
$\displaystyle \int (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}\, dx = \tfrac{1}{3}\cdot \int \sqrt[4]{x^3 + 3x + 2}\cdot 3 (x^2 + 1)\, dx =\tfrac{1}{3}\cdot \int \sqrt[4]{z}\, dz=\ldots$