Hello. I asked Wolfram Alpha the question shown below. Shown below is exactly what I typed into the Wolfram Alpha query field. (I also typed into the query field variations of the text below. I got the same result.)

Integrate[Sqrt[1- x^2], x]

Here's the answer it gave me. (For each expression below, the format is Wolfram language plain text.)

(x Sqrt[1- x^2])/2- ArcTan[Sqrt[1- x^2]/(1+ x)]

IMO the above answer is wrong.

I used Mathematica and here's the answer it gave me:

(x Sqrt[1- x^2]+ ArcSin[x])/2

IMO the answer directly above is the correct one.

I also solved the integral by hand, using trig substitution (it's a well-known integral), and I got the same answer that Mathematica gave me.

Would someone please explain. Or at least, would someone please ask Wolfram Alpha the same question shown above, and tell us the result. IMO the result should not contain the ArcTan function. It should contain the ArcSin function.