How To Integrate 1/sqrt(x) + x^(1/3)

\begin{array}{l} \int \frac{d x}{\sqrt{x} + \sqrt[3]{x}} \\ B y S u b s t i t u t i o n \\ S u p p o s e \Rightarrow z^{6} = x, n o t e \dots L C D [2, 3] = 6 \\ 6 z^{5} d z = d x \\ \int \frac{6 z^{5}}{z^{3} + z^{2}} d z \\ 6 \int \frac{z^{3}}{z^{} + 1} d z \end{array}

\begin{array}{l} 6 \int z^{2} - z + 1 - \frac{1}{z^{} + 1} d z \\ \Rightarrow 6 (\frac{z^{3}}{3} - \frac{z^{2}}{2} + z - \ln | z + 1 |) + c \\ \Rightarrow 6 (\frac{\sqrt{x}}{3} - \frac{\sqrt[3]{x}}{2} + \sqrt[6]{x} - \ln | \sqrt[6]{x} + 1 |) + c \end{array}