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

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

Step by step solution

Problem

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

Show full step-by-step solution

Answer

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

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

Main topic:

Integrals by partial fraction expansion

Used formulas:

2. See formulas

Time to solve it:

0.35 seconds