How does Wolfram Alpha come up with the substitution $x = 2\sin u$? Integration/Analysis I have to integrate 
$$
\int_0^2 \sqrt{4-x^2} \, dx
$$
I looked at the Wolfram Alpha step by step solution, and first thing it does is it substitutes
$x = 2\sin(u)\text{ and } \,dx = 2\cos(u)\,du$
How does it know to substitute $2\sin(u)$ for $x$?

This is a common substitution technique known as Trig substitution, you substitute $x$ with a trigonometric function.
Typically, when something is in the form $\sqrt{a-x^2}$, you substitute $x=\sqrt a\sin u$ 
