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\int\frac{7}{x^2+3x-10}dx

Integral of 7/(3x-10+x^2)

Answer

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

Step-by-step explanation

Problem

$\int\frac{7}{x^2+3x-10}dx$
1

Factor the trinomial $-10+3x+x^2$ finding two numbers that multiply to form $-10$ and added form $3$

$\begin{matrix}\left(-2\right)\left(5\right)=-10\\ \left(-2\right)+\left(5\right)=3\end{matrix}$

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Answer

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