Final answer to the problem
The integral diverges.
Step-by-step Solution
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1
Rewrite the expression $\frac{x+18}{x^2+x-12}$ inside the integral in factored form
$\int\frac{x+18}{\left(x-3\right)\left(x+4\right)}dx$
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$\int\frac{x+18}{\left(x-3\right)\left(x+4\right)}dx$
Learn how to solve problems step by step online. int((x+18)/(x^2+x+-12))dx&4&infinity. Rewrite the expression \frac{x+18}{x^2+x-12} inside the integral in factored form. Rewrite the fraction \frac{x+18}{\left(x-3\right)\left(x+4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{3}{x-3}+\frac{-2}{x+4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{3}{x-3}dx results in: 3\ln\left(x-3\right).
Final answer to the problem
The integral diverges.
