Find the integral
Rewrite the integrand $\left(x+1\right)\left(x-4\right)$ in expanded form
Expand the integral $\int\left(x^2-3x-4\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$
The integral $\int-3xdx$ results in: $-\frac{3}{2}x^2$
The integral $\int-4dx$ results in: $-4x$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
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