Integration Bee Training for Advanced #13.2 - Trickier Weierstrass

Memorable Timestamp:
0:18 - First Scary Example
4:56 - A Nice Satisfying Example
8:38 - A Tedious Example
12:30 - Another Tedious Example
16:29 - A Very Tricky Example

[@bra1nwave172]

8:24 lol that evaluation scared me for a sec

[@Silver-cu5up]

Lol

[@enzocoronel354]

11:12 from this moment you could separate into 2 integrals by using u2+1=(u2+1)+1 and then distributing the denominator. This separation allows you to complexify one of the integrals with u=tanθ and the other one gets easier because is an arctan. After adding the integrals and then multiplying by 4 I got π.

[@Silver-cu5up]

How do you complexify dθ/(3tan^2θ+1) nicely???

[@enzocoronel354]

@@Silver-cu5up dθ/(3tan^2θ+1) = dθ/(3(sin^2θ)/(cos^2θ)+1) = cos^2θ.dθ/3(sin^2θ)+(cos^2θ) = complexifying = (2cos(2θ)+2)dθ/(-6cos(2θ)-6)+(2cos(2θ)+2)

[@Silver-cu5up]

@@enzocoronel354 ohhhhhhhh, gotcha

[@joshpradhan3292]

8:38
3+cosx = (cosx - 2) + 5 in the numerator and then you split to get a t sub with a cosx in just the denominator.

[@Silver-cu5up]

That definitely would be faster!! 0o0