Learn how to solve problems step by step online. Find the integral int(1/(x+2(x^2+1)))dx. Solve the product 2\left(x^2+1\right). Rewrite the expression \frac{1}{x+2x^2+2} inside the integral in factored form. Take the constant \frac{1}{2} out of the integral. We can solve the integral \int\frac{1}{\left(x+\frac{1}{4}\right)^2+\frac{15}{16}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+\frac{1}{4} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

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