# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{x^2+2}{\left(x+1\right)^2\left(x+1\right)\left(x-2\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (x^2+2)/((x+1)^2(x+1)*(x-2)) with respect to x. When multiplying exponents with same base you can add the exponents: \left(x+1\right)^2\left(x+1\right)\left(x-2\right). Rewrite the fraction \frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)} in 4 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(x+1\right)^{3}\left(x-2\right). Multiplying polynomials.

$\frac{1}{2\left(x+1\right)^{2}}+\frac{2}{9}\ln\left|x-2\right|-\frac{2}{9}\ln\left|x+1\right|+\frac{-\frac{1}{3}}{x+1}+C_0$

### Problem Analysis

$\int\frac{x^2+2}{\left(x+1\right)^2\left(x+1\right)\left(x-2\right)}dx$

### Main topic:

Integrals by partial fraction expansion

~ 2.64 seconds