Exercise
$\int sen^32x\cdot\cos^2\left(x\right)dx$
Step-by-step Solution
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(2x)^3cos(x)^2)dx. Rewrite the trigonometric expression \sin\left(2x\right)^3\cos\left(x\right)^2 inside the integral. The integral of a function times a constant (8) is equal to the constant times the integral of the function. Apply the formula: \int\sin\left(\theta \right)^n\cos\left(\theta \right)^mdx=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)^{\left(m+1\right)}}{n+m}+\frac{n-1}{n+m}\int\sin\left(\theta \right)^{\left(n-2\right)}\cos\left(\theta \right)^mdx, where m=5 and n=3. Simplify the expression.
Solve the trigonometric integral int(sin(2x)^3cos(x)^2)dx
Final answer to the exercise
$-\sin\left(x\right)^{2}\cos\left(x\right)^{6}-\frac{1}{3}\cos\left(x\right)^{6}+C_0$