@owl3math Thanks for confirming, I tried to prove the formula starting with bounds 0 to ∞ but it only worked once I changed it to -∞ to ∞. Then only after adding the condition f(x) is even, I could get the result shown in the video. Btw I have some cool integrals I think you should try (0 to π/2) ∫ ln(1 + 4sin²(x)) dx and (0 to ∞) ∫ cos(x) / (x⁴ + 1) dx
The first move - rewriting it in the form of Labochevsky is genius 😊
That part is key!
Excellent 👌
Hi Slavino. Thanks! 🙏
Genius i am bewilderd by yr cerebral
thanks Ashish ☺
Correct me if I'm wrong but isn't the formula with lower bounds -∞, and -π/2? I think the version you showed works only if f(x) is an even function
Hi Samir. Yes, the f(x) must be even for Lobachevsky to work.
@owl3math Thanks for confirming, I tried to prove the formula starting with bounds 0 to ∞ but it only worked once I changed it to -∞ to ∞. Then only after adding the condition f(x) is even, I could get the result shown in the video.
Btw I have some cool integrals I think you should try (0 to π/2) ∫ ln(1 + 4sin²(x)) dx and (0 to ∞) ∫ cos(x) / (x⁴ + 1) dx
pleaase/ pdf
Hello. This one didn't come from an integration bee. Are you looking for a link to something?