Antiderivative of 4-3(1+x^2)^-1 | Graph Comparison

[master1425]

Homework Statement

Find the antiderivative F of f that satisifies the given condition. Check by comparing the graphs of f and F.

f(x)=4-3(1+x^2)^-1
F(1)=0

Homework Equations

The Attempt at a Solution

So far what I attempted to do was this:

F(x)=4x -3tan^-1(x) + C
but was unsure from here on.

 

[Defennder]

Just plug in the given value for F(1) = 0 and solve for C.

 

[master1425]

Ok so my F(x) is correct?

That was probably the part I needed the most assurance with.

 

[HallsofIvy]

Homework Statement

Find the antiderivative F of f that satisifies the given condition. Check by comparing the graphs of f and F.

f(x)=4-3(1+x^2)^-1
F(1)=0

Homework Equations

The Attempt at a Solution

So far what I attempted to do was this:

F(x)=4x -3tan^-1(x) + C
but was unsure from here on.

(4x)'= 4 and
(-3 arctan(x))'= -3/(x²+1)
so what is F' ?

F(1)= 4(1)- 3arctan(1)+ C= 0. C= ?