integral x(x + 4) (x - 1) dx

[tex] \int\limits {x(x+4)(x-1)} \, dx \\ =\int\limits {x(x^2+3x-4)} \, dx\\ = \int\limits {x^3+3x^2-4x} \, dx\\ = \frac{1}{3+1} x^{3+1} + \frac{3}{2+1} x^{2+1} - \frac{4}{1+1} x^{1+1}+C\\ = \frac{1}{4} x^{4}+ \frac{3}{3} x^{3}- \frac{4}{2} x^{2} +C\\ \bold{= \frac{1}{4} x^{4}+ x^{3}-2 x^{2} +C }[/tex]