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Step-by-step Solution

Integral of $\frac{7}{x^2+3x-10}$ with respect to x

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Answer

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

Step-by-step explanation

Problem to solve:

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

Take the constant out of the integral

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

Factor the trinomial $-10+x^2+3x$ 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

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

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