Learn how to solve problems step by step online. Integrate int(u(1-u^2)^(1/2))du. We can solve the integral \int u\sqrt{1-u^2}du by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Substituting in the original integral, we get. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2.

Integrate int(u(1-u^2)^(1/2))du