Question

Solve

$\int \frac{dx}{\sqrt{5x+8}}$

using- (a) $u=5x+8$ (b) $u=\sqrt{5x+8}$

Answer 1

$a)u=5x+8⟹du=5dx$

$\int \frac{dx}{\sqrt{5x+8}}=\frac{1}{5}\int u^{-1/2}du=\frac{2}{5}\sqrt{u}+c=\frac{2}{5}\sqrt{5x+8}+c$

$b)u=\sqrt{5x+8}⟹du=\frac{5}{2\sqrt{5x+8}}dx$

$\int \frac{dx}{\sqrt{5x+8}}=\frac{2}{5}\int du=\frac{2}{5}u+c=\frac{2}{5}\sqrt{5x+8}+c$