Exercise
$\int\left(1+sen^3x\right)\left(senxcosx\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric integral int((1+sin(x)^3)sin(x)cos(x))dx. Simplify \left(1+\sin\left(x\right)^3\right)\sin\left(x\right)\cos\left(x\right) into \frac{2\sin\left(x\right)^{4}\cos\left(x\right)+2\cos\left(x\right)\sin\left(x\right)}{2} by applying trigonometric identities. Take the constant \frac{1}{2} out of the integral. Simplify the expression. The integral \int\sin\left(x\right)^{4}\cos\left(x\right)dx results in: \frac{\sin\left(x\right)^{5}}{5}.
Solve the trigonometric integral int((1+sin(x)^3)sin(x)cos(x))dx
Final answer to the exercise
$\frac{\sin\left(x\right)^{5}}{5}-\frac{1}{4}\cos\left(2x\right)+C_0$