Learn how to solve integral calculus problems step by step online. Find the integral int((2x^2+8x+-6)/(x^3+x^23x+3))dx. Rewrite the expression \frac{2x^2+8x-6}{x^3+x^2+3x+3} inside the integral in factored form. Rewrite the fraction \frac{2x^2+8x-6}{\left(x^{2}+3\right)\left(x+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{5x+3}{x^{2}+3}+\frac{-3}{x+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{5x+3}{x^{2}+3}dx results in: -5\ln\left(\frac{\sqrt{3}}{\sqrt{x^{2}+3}}\right)+3\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{x}{\sqrt{3}}\right).

Find the integral int((2x^2+8x+-6)/(x^3+x^23x+3))dx