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Step-by-step Solution

Integral of $\frac{6-x}{x^2\left(x^2-x\right)}$ with respect to x

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ln
log
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asin
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asinh
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Answer

$5\ln\left|x-1\right|+3x^{-2}-5\ln\left|x\right|+5x^{-1}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{\left(6-x\right)}{x^2\left(x^2-x\right)}dx$
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Factoring by $x$

$\int\frac{6-x}{x^2x\left(x-1\right)}dx$
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When multiplying exponents with same base you can add the exponents

$\int\frac{6-x}{x^{3}\left(x-1\right)}dx$

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Answer

$5\ln\left|x-1\right|+3x^{-2}-5\ln\left|x\right|+5x^{-1}+C_0$