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- Integrate by trigonometric substitution
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Divide $x^5+x^4-8$ by $x^3-4x$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{3}-4x\phantom{;};}{\phantom{;}x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x^{3}-4x\phantom{;}\overline{\smash{)}\phantom{;}x^{5}+x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-4x\phantom{;};}\underline{-x^{5}\phantom{-;x^n}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+4x^{3};}\phantom{;}x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-4x\phantom{;}-;x^n;}\underline{-x^{4}\phantom{-;x^n}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-x^{4}+4x^{2}-;x^n;}\phantom{;}4x^{3}+4x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-4x\phantom{;}-;x^n-;x^n;}\underline{-4x^{3}\phantom{-;x^n}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-4x^{3}+16x\phantom{;}-;x^n-;x^n;}\phantom{;}4x^{2}+16x\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^5+x^4+-8)/(x^3-4x))dx. Divide x^5+x^4-8 by x^3-4x. Resulting polynomial. Expand the integral \int\left(x^{2}+x+4+\frac{4x^{2}+16x-8}{x^3-4x}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.