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Step-by-step Solution

Integral of $\frac{3x-4}{x^2-4x}$ with respect to x

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\frac{3x-4}{x^2-4x}dx$
1

Split the fraction $\frac{3x+-4}{x^2-4x}$ in two terms with common denominator ($x^2-4x$)

$\int\left(\frac{3x}{x^2-4x}+\frac{-4}{x^2-4x}\right)dx$
2

The integral of the sum of two or more functions is equal to the sum of their integrals

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

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Answer

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