Step-by-step Solution

Integral of $\frac{x^4-x^3-x-1}{x^3-x^2}$ with respect to x

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Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\begin{array}{l}\phantom{\phantom{;}x^{3}-x^{2};}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{3}-x^{2}\overline{\smash{)}\phantom{;}x^{4}-x^{3}\phantom{-;x^n}-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-x^{2};}\underline{-x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3};}-x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$

Unlock this full step-by-step solution!

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of (x^4-x^3-x-1)/(x^3-x^2) with respect to x. Divide x^4-x^3-x-1 by x^3-x^2. Resulting polynomial. The integral of the sum of two or more functions is equal to the sum of their integrals. The integral \int xdx results in: \frac{1}{2}x^2.

Final Answer

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

Problem Analysis