Question

Solve${\int }^{}\left(2x+1\right)\sqrt{x-4}dx$

Answer 1

$\int \left(2x+1\right)\sqrt{x-4}dx$

Put $x-4=u$

$dx=du$

$\int \left(2u^{3/2}+9u^{1/2}\right)du$

$2\frac{u^{5/2}}{5/2}+9\frac{u^{3/2}}{3/2}+C$

$\frac{4}{5}{\left(x-4\right)}^{5/2}+6{\left(x-4\right)}^{3/2}+C$

$2{\left(x-4\right)}^{3/2}\left[2\left(x-4\right)+15\right]+C$

$\frac{2}{5}{\left(x-4\right)}^{3/2}\left(2x+7\right)+C$