Question

For x where the denominator is nonzero, which method finds the general antiderivative of the expression below?

$$\frac{1}{x^{2}+18x+82}$$

Accepted Answer

$$\begin{aligned}&	ext{complete the square as }(x+9)^{2}+1\ &	ext{then use }\arctan\end{aligned}$$

Answer

$$	ext{use }\ln|x+9|	ext{ without matching its derivative}$$

Answer

$$	ext{factor the denominator over the reals into linear factors}$$

Answer

$$	ext{integrate the denominator as a power without changing the fraction}$$

Practice: Integration - Rational Preparation Method