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

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