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.

Answer and Explanation:

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}


Learn more about this topic:

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Indefinite Integrals as Anti Derivatives

from Math 104: Calculus

Chapter 12 / Lesson 11
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