Good

Rigged for Lola

Now me next

mashallah

🐐

ALMA, add back being able to see our daily earnings by hovering over our graph, PLEASE

Why take it away? You dingle

Jep

guns of glory city 28 not paying

nerfed lottery but msg still says 5 mins 250

Hi

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