Learn how to solve problems step by step online. Integrate int(z^(1/2)(z^2+-1/(4z)))dz. We can solve the integral \int\sqrt{z}\left(z^2+\frac{-1}{4z}\right)dz 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 4z it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dz in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by finding the derivative of the equation above. Isolate dz in the previous equation. Rewriting z in terms of u.

Integrate int(z^(1/2)(z^2+-1/(4z)))dz