How to Integrate 1/x+x sqrt(x)

\begin{array}{l} \int \frac{1}{x + x \sqrt{x}} d x \\ B y S u b s t i t u t i o n \\ S u p p o s e \Rightarrow z^{2} = x \\ 2 z d z = d x \\ \int \frac{2 z}{z^{2} + z^{3}} d x \\ \int \frac{2}{z (z^{} + 1)} d x \\ B y U s i n g P a r t i a l F r a c t i o n \\ \int \frac{2}{z (z^{} + 1)} d x = \frac{A}{z} + \frac{B}{z + 1} \\ L e t \Rightarrow z = 0 \Rightarrow A = 2 \\ L e t \Rightarrow z = - 1 \Rightarrow B = - 2 \\ \int \frac{2}{z} - \frac{2}{z + 1} d x \\ 2 \ln | z | - 2 \ln | z + 1 | + c \\ \Rightarrow 2 \ln | \sqrt{x} | - 2 \ln | \sqrt{x} + 1 | + c \end{array}