Final Answer
$\frac{-1}{2x}+\frac{1}{4}\ln\left(x+2\right)-\frac{1}{4}\ln\left(x\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{1}{x^2\left(x+2\right)}dx$
Specify the solving method
1
Rewrite the fraction $\frac{1}{x^2\left(x+2\right)}$ in $3$ simpler fractions using partial fraction decomposition
$\frac{1}{x^2\left(x+2\right)}=\frac{A}{x^2}+\frac{B}{x+2}+\frac{C}{x}$
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$\frac{1}{x^2\left(x+2\right)}=\frac{A}{x^2}+\frac{B}{x+2}+\frac{C}{x}$
Learn how to solve problems step by step online. Find the integral int(1/(x^2(x+2)))dx. Rewrite the fraction \frac{1}{x^2\left(x+2\right)} 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 x^2\left(x+2\right). Multiplying polynomials. Simplifying.
Final Answer
$\frac{-1}{2x}+\frac{1}{4}\ln\left(x+2\right)-\frac{1}{4}\ln\left(x\right)+C_0$