Final answer to the problem
Step-by-step Solution
Specify the solving method
We can solve the integral $\int\frac{2}{3}\left(\frac{\sin\left(x\right)^3\cos\left(x\right)}{\sqrt{1-\sin\left(x\right)^2}}\right)dx$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution
Learn how to solve problems step by step online.
$t=\tan\left(\frac{x}{2}\right)$
Learn how to solve problems step by step online. Solve the trigonometric integral int(2/3(sin(x)^3cos(x))/((1-sin(x)^2)^1/2))dx. We can solve the integral \int\frac{2}{3}\left(\frac{\sin\left(x\right)^3\cos\left(x\right)}{\sqrt{1-\sin\left(x\right)^2}}\right)dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.