Exercise
$\int\left(x^2+3x\right)\cdot\left(x+2\right)^{-5}$
Step-by-step Solution
Learn how to solve integral calculus problems step by step online. Find the integral int((x^2+3x)(x+2)^(-5))dx. Multiplying polynomials \left(x+2\right)^{-5} and x^2+3x. Expand the integral \int\left(\left(x+2\right)^{-5}x^2+3\left(x+2\right)^{-5}x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\left(x+2\right)^{-5}x^2dx results in: \frac{1}{-2\left(x+2\right)^{2}}+\frac{4}{3\left(x+2\right)^{3}}+\frac{-1}{\left(x+2\right)^{4}}. Gather the results of all integrals.
Find the integral int((x^2+3x)(x+2)^(-5))dx
Final answer to the exercise
$\frac{-1}{\left(x+2\right)^{4}}+\frac{4}{3\left(x+2\right)^{3}}+\frac{1}{-2\left(x+2\right)^{2}}+\frac{3}{2\left(x+2\right)^{4}}+\frac{-1}{\left(x+2\right)^{3}}+C_0$