Final Answer
Step-by-step Solution
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Divide $x^3-1$ by $4x^3-x$
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$\begin{array}{l}\phantom{\phantom{;}4x^{3}-x\phantom{;};}{\phantom{;}\frac{1}{4}\phantom{;}\phantom{;}}\\\phantom{;}4x^{3}-x\phantom{;}\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x^{3}-x\phantom{;};}\underline{-x^{3}\phantom{-;x^n}+\frac{1}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+\frac{1}{4}x\phantom{;};}\phantom{;}\frac{1}{4}x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((x^3-1)/(4x^3-x))dx. Divide x^3-1 by 4x^3-x. Resulting polynomial. Expand the integral \int\left(\frac{1}{4}+\frac{\frac{1}{4}x-1}{4x^3-x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{4}dx results in: \frac{1}{4}x.