## Thomas' Calculus 13th Edition

$\int \frac{(1 + \sqrt{x})^{\frac{1}{3}}}{\sqrt{x}} dx = \frac{3}{2}(1+\sqrt{x})^\frac{4}{3} + C$
$\int \frac{(1 + \sqrt{x})^{\frac{1}{3}}}{\sqrt{x}} dx\space$ and $\space u = 1 + \sqrt{x}$ $du = \frac{1}{2\sqrt{x}}dx$ Doing the substitution $\space u = 1 + \sqrt{x}$ $\int (u)^{\frac{1}{3}} 2du\space$ => $\space2\int u^\frac{1}{3} du$ Applying the power rule for integrals $2\int u^\frac{1}{3} du = \frac{3}{2}u^\frac{4}{3} + C$ Backing to x $\int \frac{(1 + \sqrt{x})^{\frac{1}{3}}}{\sqrt{x}} dx = \frac{3}{2}(1+\sqrt{x})^\frac{4}{3} + C$