i just won 2 in the last 3 this is kind of nutty yo

3 in the last 4 now

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

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Yo

Plis add more offerwall

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withdraw

go to withdraw section

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Hi

Hi