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- Integrate by partial fractions
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Divide $2x^5-10x^3-2x^2+10$ by $x^2-5$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-5;}{\phantom{;}2x^{3}\phantom{-;x^n}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-5\overline{\smash{)}\phantom{;}2x^{5}\phantom{-;x^n}-10x^{3}-2x^{2}\phantom{-;x^n}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-5;}\underline{-2x^{5}\phantom{-;x^n}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}+10x^{3};}-2x^{2}\phantom{-;x^n}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-5-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{2}-10\phantom{;}\phantom{;}-;x^n;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x^5-10x^3-2x^2+10)/(x^2-5))dx. Divide 2x^5-10x^3-2x^2+10 by x^2-5. Resulting polynomial. Expand the integral \int\left(2x^{3}-2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2x^{3}dx results in: \frac{1}{2}x^{4}.
