Question

Find the integral of $\int \frac{x^3+3x+4}{\sqrt{x}}dx$

Answer 1

$\int \frac{x^3+3x+4}{\sqrt{x}}dx$
$=\int (x^{\frac{5}{2}}+3x^{\frac{1}{2}}+4x^{-\frac{1}{2}})dx$
$=\frac{x^{\frac{7}{2}}}{\frac{7}{2}}+\frac{3\left(x^{\frac{3}{2}}\right)}{\frac{3}{2}}+\frac{4\left(x^{\frac{1}{2}}\right)}{\frac{1}{2}}+C$
$=\frac{2}{7}{x}^{\frac{7}{2}}+2x^{\frac{3}{2}}+8x^{\frac{1}{2}}+C$
$=\frac{2}{7}{x}^{\frac{7}{2}}+2x^{\frac{3}{2}}+8\sqrt{x}+C$