Final Answer
$-\ln\left(x\right)+\frac{3}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+1\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{5x+3}{x^3-2x^2-3x}dx$
Specify the solving method
1
Rewrite the expression $\frac{5x+3}{x^3-2x^2-3x}$ inside the integral in factored form
$\int\frac{5x+3}{x\left(x-3\right)\left(x+1\right)}dx$
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$\int\frac{5x+3}{x\left(x-3\right)\left(x+1\right)}dx$
Learn how to solve problems step by step online. Find the integral int((5x+3)/(x^3-2x^2-3x))dx. Rewrite the expression \frac{5x+3}{x^3-2x^2-3x} inside the integral in factored form. The integral \int\frac{-1}{x}dx results in: -\ln\left(x\right). The integral \int\frac{3}{2\left(x-3\right)}dx results in: \frac{3}{2}\ln\left(x-3\right). The integral \int\frac{-1}{2\left(x+1\right)}dx results in: -\frac{1}{2}\ln\left(x+1\right).
Final Answer
$-\ln\left(x\right)+\frac{3}{2}\ln\left(x-3\right)-\frac{1}{2}\ln\left(x+1\right)+C_0$