Exercise
$\int2\sin^2\left(x\right)cos^2\left(x\right)dx$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the trigonometric integral int(2sin(x)^2cos(x)^2)dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the trigonometric expression \sin\left(x\right)^2\cos\left(x\right)^2 inside the integral. Expand the integral \int\left(\cos\left(x\right)^2-\cos\left(x\right)^{4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Multiply the single term 2 by each term of the polynomial \left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right).
Solve the trigonometric integral int(2sin(x)^2cos(x)^2)dx
Final answer to the exercise
$\frac{1}{2}\sin\left(2x\right)+\frac{3}{2}x-\frac{3}{8}\sin\left(2x\right)-\frac{1}{2}\cos\left(x\right)^{3}\sin\left(x\right)+C_0$