Question

Integrate the following functions.
$\int \sqrt{ax+b}$ dx.

Answer 1

$\int \sqrt{ax+b}dx=\int (ax+b{)}^{\frac{1}{2}}dx[\because \int (ax+b{)}^{n}dx=\frac{(ax+b{)}^{n+1}}{a(n+1)}]=\frac{(ax+b{)}^{\left(\frac{1}{2}\right)+1}}{a(\frac{1}{2}+1)}+C=\frac{(ax+b{)}^{\frac{3}{2}}}{a\left(\frac{3}{2}\right)}+C=\frac{2}{3a}(ax+b{)}^{\frac{3}{2}}+C$