Step-by-step Solution

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Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

$\int\frac{x-8}{x^{3}}dx$

Learn how to solve integrals of rational functions problems step by step online. Integral of (x-8)/(x(x^2-4x+4x)) with respect to x. Simplifying. Split the fraction \frac{x-8}{x^{3}} inside the integral, in two terms with common denominator x^{3}. Simplifying. The integral \int\frac{1}{x^{2}}dx results in: \frac{-1}{x}.

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

Problem Analysis

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

Main topic:

Integrals of Rational Functions

~ 0.28 seconds