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

Integral of (2x+5)/(5x-7+x^2)

Answer

$2\int\frac{x}{\left(\frac{5}{2}+x\right)^2-\frac{53}{4}}dx-\frac{20}{53}v+5\ln\left|1-\frac{4}{53}v\right|$

Step-by-step explanation

Problem

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

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$\int\frac{5+2x}{-\frac{25}{4}+\frac{25}{4}-7+5x+x^2}dx$

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Answer

$2\int\frac{x}{\left(\frac{5}{2}+x\right)^2-\frac{53}{4}}dx-\frac{20}{53}v+5\ln\left|1-\frac{4}{53}v\right|$