Question

∫ t(2t-3√t)dt

Answer 1

Let us rewrite$\int t (2 t - 3 \sqrt{t}) dt$ as $\int (2 t^2 - 3 t^{3/2}) dt$.

Using table integral $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, obtain:

$\int (2 t^2 - 3 t^{3/2}) dt = 2 \frac{t^3}{3} - 3 \cdot \frac{2}{5} t^{5/2} + C = \frac{2}{3}t^{3} - \frac{6}{5} t^{5/2} + C$.