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\int\frac{3x^2+6x+2}{x^2+3x+2}dx

Integral of (6x+2+3x^2)/(3x+2+x^2)

Answer

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

Step-by-step explanation

Problem

$\int\frac{3x^2+6x+2}{x^2+3x+2}dx$
1

Divide $2+6x+3x^2$ by $2+3x+x^2$

$\left|\begin{matrix}3x^{2} & 6x & 2 \\ -3x^{2} & -9x & -6 \\ & -3x & -4\end{matrix}\right|\begin{matrix}x^{2}+3x+2 \\ 3 \\ \\ \end{matrix}$

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Answer

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

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