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

Integral of (2x^2-3)/((x+1)^2(x+2)^2)

Answer

$\frac{-5}{2+x}+\frac{1}{1+x}+2\ln\left|2+x\right|-2\ln\left|1+x\right|+C_0$

Step-by-step explanation

Problem

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

Using partial fraction decomposition, the fraction $\frac{2x^2-3}{\left(2+x\right)^2\left(1+x\right)^2}$ can be rewritten as

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

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Answer

$\frac{-5}{2+x}+\frac{1}{1+x}+2\ln\left|2+x\right|-2\ln\left|1+x\right|+C_0$