Exercise
$\int5sin\left(x\right)cos^2\left(x\right)dx$
Step-by-step Solution
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(5sin(x)cos(x)^2)dx. Simplify 5\sin\left(x\right)\cos\left(x\right)^2 into 5\sin\left(x\right)-5\sin\left(x\right)^{3} by applying trigonometric identities. Expand the integral \int\left(5\sin\left(x\right)-5\sin\left(x\right)^{3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5\sin\left(x\right)dx results in: -5\cos\left(x\right). The integral \int-5\sin\left(x\right)^{3}dx results in: \frac{5\sin\left(x\right)^{2}\cos\left(x\right)}{3}+\frac{10}{3}\cos\left(x\right).
Solve the trigonometric integral int(5sin(x)cos(x)^2)dx
Final answer to the exercise
$-\frac{5}{3}\cos\left(x\right)+\frac{5\sin\left(x\right)^{2}\cos\left(x\right)}{3}+C_0$