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\int\frac{5x^2+3}{x^2-2x-3}dx

Integral of (5x^2+3)/(-2x-3+x^2)

Answer

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

Step-by-step explanation

Problem

$\int\frac{5x^2+3}{x^2-2x-3}dx$
1

Factor the trinomial $-3-2x+x^2$ finding two numbers that multiply to form $-3$ and added form $-2$

$\begin{matrix}\left(-3\right)\left(1\right)=-3\\ \left(-3\right)+\left(1\right)=-2\end{matrix}$

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Answer

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

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$\int\frac{5x^2+3}{x^2-2x-3}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

6. See formulas

Time to solve it:

0.82 seconds