Question

Evaluate $\int \left(\frac{x^2+3x+4}{\sqrt{x}}\right)dx$

Answer 1

$\int \left(\frac{x^2+3x+4}{\sqrt{x}}\right)dx$

$\Rightarrow \int (x{)}^{2-\frac{1}{2}}+3(x{)}^{1-\frac{1}{2}}+4\left(x\right)\frac{-1}{2}$

$\Rightarrow \int x^{3/2}+3x^{1/2}+4x^{-1/2}dx$

$\Rightarrow \frac{2}{5}{x}^{5/2}+2x^{3/2}+8x^{1/2}+c.$