Learn how to solve integrals with radicals problems step by step online. Integrate int((x^2-4x+8)^(1/2))dx. Rewrite the expression \sqrt{x^2-4x+8} inside the integral in factored form. We can solve the integral \int\sqrt{\left(x-2\right)^2+4}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.

Integrate int((x^2-4x+8)^(1/2))dx