Question

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

 

Answer 1

\[\int\sqrt{x}\left( 3 - 5x \right)dx\]
\[ = \int x^\frac{1}{2} \left( 3 - 5x \right)dx\]
\[ = \int\left( 3 x^\frac{1}{2} - 5 x^\frac{3}{2} \right)dx\]
\[ = 3\left[ \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} \right] - 5\left[ \frac{x^\frac{3}{2} + 1}{\frac{3}{2} + 1} \right] + C\]
\[ = 2 x^\frac{3}{2} - 2 x^\frac{5}{2} + C\]