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

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

Answer

$5x+12\ln\left|x-3\right|-2\ln\left|x+1\right|+C_0$

Step-by-step explanation

Problem to solve:

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

Divide $5x^2+3$ by $x^2-2x-3$

$\left|\begin{matrix}5x^{2} & & 3 \\ -5x^{2} & 10x & 15 \\ & 10x & 18\end{matrix}\right|\begin{matrix}x^{2}-2x-3 \\ 5 \\ \\ \end{matrix}$

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Answer

$5x+12\ln\left|x-3\right|-2\ln\left|x+1\right|+C_0$

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