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Step-by-step Solution

Integral of (3x-4)/(x^2-4x)

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Answer

$\ln\left|x\right|+2\ln\left|x-4\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{3x-4}{x^2-4x}dx$
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Factoring by $x$

$\int\frac{3x-4}{x\left(x-4\right)}dx$
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Rewrite the fraction $\frac{3x-4}{x\left(x-4\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{3x-4}{x\left(x-4\right)}=\frac{A}{x}+\frac{B}{x-4}$

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Answer

$\ln\left|x\right|+2\ln\left|x-4\right|+C_0$

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