Question

what's the integration of 1/(x^2+1)

Answer 1

You want the anti derivative?

Answer 2

yes

Answer 3

Trig sub \(x=\tan\theta\)

Answer 4

\(dx=\sec^2\theta d\theta\)

Answer 5

\[
\frac{dx}{x^2+1}=\frac{\sec^2\theta d\theta}{\sec^2\theta}=d\theta
\]

Answer 6

Remember that \(d\theta = \theta'dx\)

Answer 7

This means \[

\theta' = \frac{1}{x^2+1}

\]So \(\theta\) is the anti derivative.

Answer 8

U don't have to use trig sub, 1/x^2+1 us the derivative of arctanx so it's integration is arctanx

Answer 9

We just need \(\theta(x)\)

Answer 10

Is*

Answer 11

Since \(x=\tan(\theta)\), then \(\theta(x) = \arctan(x)\)

Answer 12

wio just made it complicated xD

Answer 13

@shamil98 that what iam trying to say :)