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Step-by-step Solution

Integral of $\frac{x-8}{x\left(x^2-4x+4x\right)}$ with respect to x

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Answer

$-x^{-1}+4x^{-2}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{x-8}{x\left(x^2-4x+4x\right)}dx\right)$
1

Adding $-4x$ and $4x$

$\int\frac{x-8}{x\left(x^2+0x\right)}dx$
2

Any expression multiplied by $0$ is equal to $0$

$\int\frac{x-8}{x\left(x^2+0\right)}dx$

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Answer

$-x^{-1}+4x^{-2}+C_0$
$\int\left(\frac{x-8}{x\left(x^2-4x+4x\right)}dx\right)$

Main topic:

Integrals of Rational Functions

Used formulas:

3. See formulas

Time to solve it:

~ 0.92 seconds