solution of indefinite integral

Question

What is a particular solution of the indefinite integral ∫(2)/(1-x²)dx that passes through (√3 , (Π/2)?

 

a) f(x)=√(3) tan^-1x-(Π/6)

b) f(x)=2tan^-1x-(Π/6)

c) f(x)=2tan^-1x+√(3)

Answer 1

I suspect that there the problem is misstated.  are you sure that it isn't 

 

∫(2)/(1+x2)dx

 

That integral is 2arctan(x)+C, which fits the form of the choices.

 

Assuming I suspicion is correct, then

 

(π/2)=2arctan(√3)+C

 

arctan(√3)=60 degrees, or (π/3) radians.

 

C=(π/2)-(2π/3)=-(π/6)

 

This gives an answer of

 

2arctan(x)-(π/6)

 

This is choice (b)

Answer 2

Answer. b is correct provided there is a change in question---

 

Question should be

 

Integral[(2/(1+(x^2))]dx

 

Otherwise question is wrong