Learn how to solve problems step by step online. Find the integral int((4x^3-3x^2+-3)/((x^2+3)(x+1)(x-2)))dx. Rewrite the fraction \frac{4x^3-3x^2-3}{\left(x^2+3\right)\left(x+1\right)\left(x-2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{\frac{33}{14}x+\frac{3}{14}}{x^2+3}+\frac{5}{6\left(x+1\right)}+\frac{17}{21\left(x-2\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{\frac{33}{14}x+\frac{3}{14}}{x^2+3}dx results in: -\frac{33}{14}\ln\left(\frac{\sqrt{3}}{\sqrt{x^2+3}}\right)+\frac{3\arctan\left(\frac{x}{\sqrt{3}}\right)}{14\sqrt{3}}. The integral \int\frac{5}{6\left(x+1\right)}dx results in: \frac{5}{6}\ln\left(x+1\right).

Find the integral int((4x^3-3x^2+-3)/((x^2+3)(x+1)(x-2)))dx