Evaluate the following indefinite integral using the method of Partial Fractions.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx$

Set up an expression that gives the correct form for a partial fraction decomposition of the integrand. For your unknown constants, use letters chosen from $A,B,C,D,$ and $F.$

$\frac{-x^2+12x+12}{(x-3)(x^2+4)}=$

$$

$2.$ Find the unknown constants, then rewrite the integral using the partial fraction decomposition.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

$$

$3.$ Use the partial fraction decomposition to find the antiderivative of the original rational expression.

Use $+K$ for the constant of integration.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx=$

$$

Practice Another Version to get another random partial fractions problem.Evaluate the following indefinite integral using the method of Partial Fractions.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx$

Set up an expression that gives the correct form for a partial fraction decomposition of the integrand. For your unknown constants, use letters chosen from $A,B,C,D,$ and $F.$

$\frac{-x^2+12x+12}{(x-3)(x^2+4)}=$

$$

$2.$ Find the unknown constants, then rewrite the integral using the partial fraction decomposition.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

$$

$3.$ Use the partial fraction decomposition to find the antiderivative of the original rational expression.

Use $+K$ for the constant of integration.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x^2+12x+12}{(x-3)(x^2+4)}dx=$

$$

Practice Another Version to get another random partial fractions problem.