Final answer to the problem
$\frac{-3-4x^{2}\ln\left|x+3\right|+2x}{x^{2}}+C_0$
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Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((18-(4x^3+2x^2))/(x^4+3x^3))dx. Rewrite the expression \frac{18-\left(4x^3+2x^2\right)}{x^4+3x^3} inside the integral in factored form. Solve the product -\left(4x^3+2x^2\right). Rewrite the fraction \frac{18-4x^3-2x^2}{x^{3}\left(x+3\right)} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{6}{x^{3}}+\frac{-4}{x+3}+\frac{-2}{x^{2}}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$\frac{-3-4x^{2}\ln\left|x+3\right|+2x}{x^{2}}+C_0$
