Exercise
$\int\frac{2x^2-5}{x^4+5x^2+6}dx$
Step-by-step Solution
Learn how to solve logarithmic equations problems step by step online. Find the integral int((2x^2-5)/(x^4+5x^2+6))dx. Rewrite the expression \frac{2x^2-5}{x^4+5x^2+6} inside the integral in factored form. Take the constant \frac{1}{y^2+5y+6} out of the integral. Expand the integral \int\left(2x^2-5\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Factor the trinomial y^2+5y+6 finding two numbers that multiply to form 6 and added form 5.
Find the integral int((2x^2-5)/(x^4+5x^2+6))dx
Final answer to the exercise
$\frac{2x^{3}-15x}{3\left(y+2\right)\left(y+3\right)}+C_0$