Question

find \\(\int (x + 3)(x - 4) dx\\) \\(\boxed{}\\) + c

Explanation:

Step1: Expand the integrand

$(x+3)(x-4) = x^2 -4x +3x -12 = x^2 -x -12$

Step2: Integrate term-by-term

$\int (x^2 -x -12)dx = \int x^2 dx - \int x dx - \int 12 dx$

Step3: Apply power rule for integration

$\int x^2 dx = \frac{x^3}{3}$, $\int x dx = \frac{x^2}{2}$, $\int 12 dx = 12x$

Answer:

$\frac{x^3}{3} - \frac{x^2}{2} - 12x$