Learn how to solve problems step by step online. Integrate int((4x^2+12x+9)^(1/3))dx. The trinomial 4x^2+12x+9 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can solve the integral \int\sqrt[3]{\left(2x+3\right)^{2}}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 2x+3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

Integrate int((4x^2+12x+9)^(1/3))dx