Exercise
$\int_{-2}^{-1}\frac{4x^2+7x+4}{x^3+2x^2+2x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (4x^2+7x+4)/(x^3+2x^22x) from -2 to -1. Rewrite the expression \frac{4x^2+7x+4}{x^3+2x^2+2x} inside the integral in factored form. Rewrite the fraction \frac{4x^2+7x+4}{x\left(x^2+2x+2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int_{-2}^{-1}\left(\frac{2}{x}+\frac{2x+3}{x^2+2x+2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-2}^{-1}\frac{2}{x}dx results in: undefined.
Integrate the function (4x^2+7x+4)/(x^3+2x^22x) from -2 to -1
Final answer to the exercise
The integral diverges.