Final Answer
$\frac{1}{2}x^2+4x+\frac{61}{3}\ln\left(x-5\right)+\frac{2}{3}\ln\left(x+1\right)+C_0$
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Step-by-step Solution
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1
Rewrite the expression $\frac{x^4-3x}{x^3-4x^2-5x}$ inside the integral in factored form
$\int\frac{x^4-3x}{x\left(x-5\right)\left(x+1\right)}dx$
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$\int\frac{x^4-3x}{x\left(x-5\right)\left(x+1\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^4-3x)/(x^3-4x^2-5x))dx. Rewrite the expression \frac{x^4-3x}{x^3-4x^2-5x} inside the integral in factored form. Rewrite the expression \frac{x^4-3x}{x\left(x-5\right)\left(x+1\right)} inside the integral in factored form. Multiply the single term x^2+\sqrt[3]{3}x+\sqrt[3]{9} by each term of the polynomial \left(x-\sqrt[3]{3}\right). Multiply the single term x by each term of the polynomial \left(x^2+\sqrt[3]{3}x+\sqrt[3]{9}\right).
Final Answer
$\frac{1}{2}x^2+4x+\frac{61}{3}\ln\left(x-5\right)+\frac{2}{3}\ln\left(x+1\right)+C_0$