Question

Is there a way to PROVE \(\int \frac{1}{x^2+1} \ dx = \tan^{-1}x + C \) ?

I know this is from the integration tables, sure. But where does that come from? Anybody here know enough to show it?

Answer 1

i think thats not true!!! since
\[\frac{d}{dx} \tan^{-1} x=\frac{1}{1+x^2}\]

Answer 2

Ack I got them switched... >_< One sec...

Answer 3

Good catch @mukushla ;-)

Answer 4

do a trig sub...

Answer 5

u=(1)tan^2?