Learn how to solve problems step by step online. Solve the trigonometric integral int(csc(4t)^3)dt. We can solve the integral \int\csc\left(4t\right)^3dt 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 4t 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 dt 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 dt in the previous equation. Substituting u and dt in the integral and simplify.

Solve the trigonometric integral int(csc(4t)^3)dt