Find the antiderivative F of f that satisfies the fiven condition. Check your answer by compairing the graphs of f and F.

Question

anonymous · Answer

$$f(x)=4-3(1+x^2)^{-1} ; F(1)=0$$

anonymous · Answer

I thought that by distubuting the 3 into 1+x^2 would make it easier to intergrate

cwrw238 · Answer

yes

anonymous · Answer

ok but thats where i get lost

helder_edwin · Answer

u have to integrate
$$ \large \int(4-3(1+x^2)^{-1})\,dx=
    \int\left(4-\frac{3}{1+x^2}\right)\,dx $$

anonymous · Answer

ok can you show me how to intergrate the fraction? I know the 4 once intergrated is 4x

helder_edwin · Answer

$$ \large =\int4\,dx-3\int\frac{1}{1+x^2}\,dx $$
do u know any function whose derivative is 1/(1+x^2) ??

anonymous · Answer

isn't that tan inverse?

helder_edwin · Answer

yes!!
$$ \large\frac{d}{dx}\arctan x=\frac{1}{1+x^2} $$

helder_edwin · Answer

then u got it!!!

anonymous · Answer

ok so just to make sure if i wrote this back in function form it would be 

$$f(x)=4x-arctanx+c$$

helder_edwin · Answer

$$ \large F(x)=4x-3\arctan x+c $$
yes. now use your initial condition F(1)=0 to find c

anonymous · Answer

Awesome! Thanks a ton for the help.

helder_edwin · Answer

u r welcome
don't forget to find the value of c