# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}dx$

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

$\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}=\frac{A}{x+2}+\frac{B}{\left(x+1\right)^2}+\frac{C}{x+1}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (5x^2+14x+10)/((x+2)(x+1)^2) with respect to x. Rewrite the fraction \frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x+2\right)\left(x+1\right)^2. Multiplying polynomials. Simplifying.

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

### Problem Analysis

$\int\frac{5x^2+14x+10}{\left(x+2\right)\left(x+1\right)^2}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.24 seconds