int((2)/(sqrt(4-36x^2)) dx ?

int((2)/(sqrt(4-36x^2)) dx

1 Answer
Apr 13, 2018

I=1/3sin^-1(3x)+c

Explanation:

We know that,

color(red)((1)int1/sqrt(a^2-x^2)dx=sin^-1(x/a)+c

Here,

I=int2/sqrt(4-36x^2)dx

=2/6int1/(sqrt((4/36)-x^2))dx

=1/3int1/sqrt((1/3)^2-x^2)dx...toApply(1)

=1/3sin^-1(x/(1/3))+c

=1/3sin^-1(3x)+c