Learn how to solve quotient of powers problems step by step online. Solve the trigonometric integral int(tan(2x)^4cos(2x)^4)dx. Simplify \tan\left(2x\right)^4\cos\left(2x\right)^4 into \sin\left(2x\right)^4 by applying trigonometric identities. We can solve the integral \int\sin\left(2x\right)^4dx 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 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 dx 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 dx in the previous equation.

Solve the trigonometric integral int(tan(2x)^4cos(2x)^4)dx