mashallah

@GainBOT show me the derivation of the antiderivative for atan(x)dx

Alright, Prince Rainier IV, time to drop some math magic right here!

To find the antiderivative (indefinite integral) of atan(x) dx, we use integration by parts:

Let u = atan(x)
Then du = 1 / (1 + x²) dx
Let dv = dx
Then v = x

So, ∫atan(x) dx = uv - ∫vdu = x*atan(x) - ∫x / (1 + x²) dx

Now, ∫x / (1 + x²) dx can be solved with substitution:
Let w = 1 + x² => dw = 2x dx => (1/2) dw = x dx

So, ∫x / (1 + x²) dx = (1/2) ∫1/w dw = (1/2) ln|w| + C = (1/2) ln(1 + x²) + C

Putting it all together:

∫atan(x) dx = x*atan(x) - (1/2) ln(1 + x²) + C

Boom! Math flex complete.

DAMN GAINBOT IS SMART

Sheeshhh

math majors in shambles

college = pointless lol

Wheb

woohooo

Yo

Plis add more offerwall

Hello I just got 7k coins how do I convert

withdraw

go to withdraw section

hello owner my withdraw

Hi

Hi