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Step-by-step Solution

Integral of $\frac{2x+5}{x^2+5x-7}$ with respect to u

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Answer

$\ln\left|x^2+5x-7\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{2x+5}{x^2+5x-7}dx$
1

Solve the integral $\int\frac{2x+5}{x^2+5x-7}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^2+5x-7 \\ du=\left(5+2x\right)dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{\left(5+2x\right)}=dx$

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Answer

$\ln\left|x^2+5x-7\right|+C_0$
$\int\frac{2x+5}{x^2+5x-7}dx$

Main topic:

Integrals of Rational Functions

Used formulas:

5. See formulas

Time to solve it:

~ 0.87 seconds