Question

antiderivative?

Answer 1

plz explain rule ?

Answer 2

Hmm this one is a little tricky.
Have you been introduced to Trig Substitutions yet?

I mean, this is a very common anti-derivative that will come up over and over, so it's worth your time to memorize it. But if you really want to understand where it's coming from, then that requires a little more work. :)

Answer 3

no

Answer 4

:-)

Answer 5

We can show that the DERIVATIVE of arctangent = 1/(1+x^2)

From that information, we'll be able to determine that the ANTI-DERIVATIVE of 1/(1+x^2) =arctangent + c

To be able to do it in the other direction requires a Trig Sub which is a bit tricky ^^

Start here,\[\large \text{Let} \quad y=\tan^{-1} x\]Recall that we can rewrite this as the TANGENT by switching the arguments.\[\large x=\tan y\]Let's label this on a triangle so we can reference it.