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Step-by-step Solution

Integral of $\frac{1}{x\left(x+1\right)\left(2x+3\right)}$ with respect to x

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Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

$\frac{1}{x\left(x+1\right)\left(2x+3\right)}=\frac{A}{x}+\frac{B}{x+1}+\frac{C}{2x+3}$

Unlock this full step-by-step solution!

Learn how to solve integrals of rational functions problems step by step online. Integral of 1/(x(x+1)*(2x+3)) with respect to x. Rewrite the fraction \frac{1}{x\left(x+1\right)\left(2x+3\right)} in 3 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 x\left(x+1\right)\left(2x+3\right). Multiplying polynomials. Simplifying.

Answer

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

Problem Analysis

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

Related formulas:

1. See formulas

Time to solve it:

~ 0.49 seconds