Final answer to the problem
$\frac{1}{2}\arcsin\left(x\right)+\frac{1}{2}x\sqrt{1-x^2}+C_0$
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Step-by-step Solution
Learn how to solve integrals with radicals problems step by step online. Integrate int((1-x^2)^(1/2))dx. We can solve the integral \int\sqrt{1-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, 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.
Final answer to the problem
$\frac{1}{2}\arcsin\left(x\right)+\frac{1}{2}x\sqrt{1-x^2}+C_0$
