int(2/(sqrt(16-4x^2)(2164x2 dx=?

int(2/(sqrt(16-4x^2)(2164x2 dx=?

1 Answer
Apr 14, 2018

arcsin(x/2)+Carcsin(x2)+C

Explanation:

derivative of arcsin(f(x))=(f'(x))/sqrt(1-f(x)^2)

int2/sqrt(16-4x^2)dx
=int2/(4sqrt(1-x^2/4))dx
=int(1/2)/sqrt(1-x^2/4)dx

using the format of arcsin(f(x)) derivative, if you let f(x)=x/2 then f'(x)=1/2

substituting:
=arcsin(x/2)+C