# Evaluate the indefinite integral \int (4x^2+4x-6) dx

## Question:

Evaluate the indefinite integral {eq}\int (4x^2+4x-6) dx {/eq}

## Indefinite Integrals:

The most thing to realize about evaluating indefinite integrals in particular is that since there are no bounds on such an integral, a constant of integration must be added to the anti-derivative of the expression to definite the general solution.

Given: {eq}\int 4x^2+4x-6 dx {/eq}

To evaluate the indefinite integral, the strategy is to take the anti-derivative of the expression before adding a constant of integration.

{eq}\begin{align*} \int 4x^2+4x-6 dx &= \frac{4x^{2+1}}{2+1}+\frac{4x^{1+1}}{1+1}-6x+c \text{ [Constant of integration added to anti-derivative]} \\ &= \frac{4x^3}{3}+\frac{4x^2}{2}-6x+c \\ &= \frac{4x^3}{3}+2x^2-6x+c \\ \end{align*} {/eq}