Question

\[\int \left( 3x + 4 \right)^2 dx\]

Answer 1

\[\int \left( 3x + 4 \right)^2 dx\]
\[ = \int \left( 9 x^2 + 2 \times 3x \times 4 + 16 \right)dx\]
`= 9 ∫    x^2dx + 24  ∫  x dx + 16 ∫   dx`
\[ = 9\left[ \frac{x^3}{3} \right] + 24\left[ \frac{x^2}{2} \right] + 16x + C\]
\[ = 3 x^3 + 12 x^2 + 16x + C\]