Final Answer
Step-by-step Solution
Specify the solving method
We could not solve this problem by using the method: Integrate by parts
Divide $2x^5+1$ by $x^3-4x^2-5x$
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$\begin{array}{l}\phantom{\phantom{;}x^{3}-4x^{2}-5x\phantom{;};}{\phantom{;}2x^{2}+8x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;}x^{3}-4x^{2}-5x\phantom{;}\overline{\smash{)}\phantom{;}2x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-4x^{2}-5x\phantom{;};}\underline{-2x^{5}+8x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}+8x^{4}+10x^{3};}\phantom{;}8x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-4x^{2}-5x\phantom{;}-;x^n;}\underline{-8x^{4}+32x^{3}+40x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-8x^{4}+32x^{3}+40x^{2}-;x^n;}\phantom{;}42x^{3}+40x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-4x^{2}-5x\phantom{;}-;x^n-;x^n;}\underline{-42x^{3}+168x^{2}+210x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-42x^{3}+168x^{2}+210x\phantom{;}-;x^n-;x^n;}\phantom{;}208x^{2}+210x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((2x^5+1)/(x^3-4x^2-5x))dx. Divide 2x^5+1 by x^3-4x^2-5x. Resulting polynomial. Expand the integral \int\left(2x^{2}+8x+42+\frac{208x^{2}+210x+1}{x^3-4x^2-5x}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2x^{2}dx results in: \frac{2}{3}x^{3}.