Question

find \\(\int (x + 5)(x - 4) dx\\) + c

Explanation:

Step1: Expand the integrand

$(x+5)(x-4) = x^2 -4x +5x -20 = x^2 +x -20$

Step2: Integrate term-by-term

$\int (x^2 +x -20)dx = \int x^2 dx + \int x dx - \int 20 dx$

Step3: Apply power rule for integration

$\int x^2 dx = \frac{x^3}{3}$, $\int x dx = \frac{x^2}{2}$, $\int 20 dx = 20x$

Answer:

$\frac{x^3}{3} + \frac{x^2}{2} - 20x$