How To: Antidifferentiate functions with radicals in calculus

This video demonstrates how to do anti-differentiate functions with radicals in calculus. To simply problems, try to substitute. For example, in the problem, the integral of x times the square root of x plus 2 dx. You can substitute w for everything underneath the radical: i.e. x + 2. When you simplify, it becomes: the integral of x times the square root of w dw. Now, you need to get rid of the x, which you can do with a substitution: w – 2 = x. Now, plug in the values and simplify it. The final answer should be, after simplification, 2/5 (x + 2)5/2 – 4/3 (x + 2 )3/2 + C. The key is to substitute and simplify, then you can apply basic rules of algebra.