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

Question

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

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Answer 1 · 2018-04-13T17:17:14

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

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#