Question

Evaluate $\int \left(7x-2\right)\sqrt{3x+2}dx$

Answer 1

Let $3x+2=t^2$

$x=\frac{t^2-2}{3}$

$dx=\frac{2t}{3}dt$

$7x-2=\frac{7t^2-20}{2}$

$\int (7x-2)\left(\sqrt{3x+2}\right)dx=\int (\frac{2}{9})(7t^4-20t^2)dt=\frac{2}{9}(\frac{7t^5}{5}-\frac{20t^3}{3})$