Learn how to solve implicit differentiation problems step by step online. Solve the trigonometric integral int(sin(3x)cos(e^2x))dx. Simplify \sin\left(3x\right)\cos\left(e^2x\right) into \frac{\sin\left(3x+e^2x\right)+\sin\left(2x\right)}{2} by applying trigonometric identities. Take the constant \frac{1}{2} out of the integral. Expand the integral \int\left(\sin\left(3x+e^2x\right)+\sin\left(2x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \frac{1}{2}\int\sin\left(3x+e^2x\right)dx results in: \frac{-\cos\left(3x+e^2x\right)}{2\left(3+e^2\right)}.

Solve the trigonometric integral int(sin(3x)cos(e^2x))dx