Question

$\int \sqrt{x}\left(3-5x\right)dx$

Answer 1

$$\begin{gathered} \int \sqrt{x}\left(3-5x\right)dx \\ =\int x^{\frac{1}{2}}\left(3-5x\right)dx \\ =\int \left(3x^{\frac{1}{2}}-5x^{\frac{3}{2}}\right)dx \\ =3\left[\frac{x^{{\displaystyle \frac{1}{2}}+1}}{{\displaystyle \frac{1}{2}}+1}\right]-5\left[\frac{x^{{\displaystyle \frac{3}{2}}+1}}{{\displaystyle \frac{3}{2}}+1}\right]+\mathrm{C} \\ =2x^{\frac{3}{2}}-2x^{\frac{5}{2}}+\mathrm{C} \end{gathered}$$