Question

\[\int \left( 2x - 3 \right)^5 + \sqrt{3x + 2}  \text{dx} \]

Answer 1

\[\int\left[ \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \right]dx\]
\[ = \int \left( 2x - 3 \right)^5 dx + \int \left( 3x + 2 \right)^\frac{1}{2} dx\]
\[ = \frac{\left( 2x - 3 \right)^{5 + 1}}{2\left( 5 + 1 \right)} + \frac{\left( 3x + 2 \right)^\frac{1}{2} + 1}{3\left( \frac{1}{2} + 1 \right)} + C\]
\[ = \frac{\left( 2x - 3 \right)^6}{12} + \frac{2}{9} \left( 3x + 2 \right)^\frac{3}{2} + C\]