# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{14x^3+24x}{\left(x^2+1\right)\left(x^2+2\right)}dx$

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

$\frac{14x^3+24x}{\left(x^2+1\right)\left(x^2+2\right)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+2}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (14x^3+24x)/((x^2+1)(x^2+2)) with respect to x. Rewrite the fraction \frac{14x^3+24x}{\left(x^2+1\right)\left(x^2+2\right)} in 2 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by \left(x^2+1\right)\left(x^2+2\right). Multiplying polynomials. Simplifying.

$5\ln\left|x^2+1\right|+2\ln\left|x^2+2\right|+C_0$

### Problem Analysis

$\int\frac{14x^3+24x}{\left(x^2+1\right)\left(x^2+2\right)}dx$

### Main topic:

Integrals by partial fraction expansion

~ 0.19 seconds