Evaluate: `int((1+x)^2)/(sqrt(x))\ dx`

Explanation

Solution:


=`\int \frac{1+x^{2}+2 x}{\sqrt{x}} d x`

=`\int\left(\frac{1}{\sqrt{x}}+\frac{x^{2}}{\sqrt{x}}+\frac{2 x}{\sqrt{x}}) d x`

=`\int \frac{1}{\sqrt{x}} d x+\int x^{3 / 2} d x+2 \int \sqrt{x} d x`

=`2 \sqrt{x}+\frac{2 x^{5 / 2}}{5}+2 \frac{2 x^{3 / 2}}{3}+C`

=`2 \sqrt{x}+\frac{2}{5} x^{5 / 2}+\frac{4}{3} x^{3 / 2}+C`