Learn how to solve special products problems step by step online. Solve the trigonometric integral int(cos(5y)^2sec(5y))dy. Simplify \cos\left(5y\right)^2\sec\left(5y\right) into \cos\left(5y\right) by applying trigonometric identities. We can solve the integral \int\cos\left(5y\right)dy 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 5y 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 dy 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 dy in the previous equation.

Solve the trigonometric integral int(cos(5y)^2sec(5y))dy