COUNTDOWN to 2025: 13 Integrals in 13 Days! ∫1/(sinx+cosx)^2 dx | Math with Professor V

[@mathwithprofessorv]

Which method do you prefer? Have you seen the lovely Weierstrass substitution before? Let me know in the comments!

[@KP094]

First step is the last step so many methods to use for some integral dunno which to choose

[@KewlWIS]

in general if u have anything like integral of 1/(linear function in terms of cosX and sinX) you can just write sinX and cosX in terms of tan(X/2) and proceed (basically weierstrass sub) sinX = 2tan(x/2)/(1+tan^2(x/2)) cosX = (1-tan^2(x/2))/(1+tan^2(x/2))

[@siyabongashoba9901]

yes, option 2 is awesome I have never seen it before once had that there is something like but to see it in action just saw it now thank you so much.

[@mathwithprofessorv]

So cool, right?! 😉

[@siyabongashoba9901]

Dear Prof.V, I hope you are doing well. For this one, I expended (sinx+cosx)^2 to (sin^2(x) + 2sin(x)cos(x) + cos^2(x)) then to sin(2x) + 1 after that I times by 1 = (sin(2x) - 1)/(sin(2x) - 1) then I got two integrals. 1 was the integral of sin(2x)/(sin^2(2x) - 1) which gives - 1/2 * 1/cos(2x) + C1 . 2 was integral of -1/(sin^2(2x) - 1) which gives tan(2x)/2 + C2 therefore, my final was = - 1/2 * 1/cos(2x) + tan(2x)/2 + C thank you so much for the integral of the day, let me enjoy the video.

[@VincenzoCurcio-y1z]

Buonasera. Ci sono varie tecniche per risolvere un integrale. La migliore tecnica e' quella in cui si arriva al risultato in modo piu agevole possibile evitando laboriosi e lunghi passaggi o calcoli. In questo caso io preferisco il primo. Saluti Prof. 😀

[@siyabongashoba9901]

wow option one is very creative!

[@mathwithprofessorv]

Glad you liked it! 👍🏻👍🏻

[@jaypee2558]

I got .5tan(2x) - .5sec(2x) + C. I wrote 2sinxcosx as sin(2x), then multiplied the num/den both by 1-sin(2x)

[@armanavagyan1876]

Oh hi my LOVELY PROF V☺

[@valor36az]

Awesome!

[@mathwithprofessorv]

Thanks so much! 😊

[@armanavagyan1876]

Amazing idea I'll enjoy it)

[@armanavagyan1876]

Watched all 13 VIDEO 🎇■

[@armanavagyan1876]

PROF UR LESSONS are stunning but 3 months i will be very busy KEEP UP MAKING new VIDEOS am gonna watch old and new LESSONS after 3 months)

[@mathwithprofessorv]

I’m so happy to hear you’re enjoying my lessons! Best of luck with your busy time and keep up the studying! 😄

[@user-lu6yg3vk9z]

@@mathwithprofessorvsimpler method is to factor out a cosx then have sec^2(x) up to with (tanx+1)^2 on the botttom

[@tonybluefor]

I didn't know the Weierstrass substitution and I was a little bit lost with this integral, looking for some trig identities😓

[@mathwithprofessorv]

Don’t fret! The Weierstrass substitution isn’t commonly taught in most calculus 2 courses, but definitely get those trig basics locked in. This video should help: Precalculus: Trigonometric Identities (Section 7.4) | Math with Professor V kzbin.info/www/bejne/iX25o4F9npZ1qJI

[@dnd2008yi]

I got -1/2cot(x+π/4)

[@avielabc604]

I solved it alittle differently I turned 2sinxcosx to sin2x then I let u =2x so du/2=dx and then I multiplied the numerator and denominator by (1- sinu) and got 0.5 integral of ( sec^2(u) -sec(u)tan(u) ) so my final answer was 0.5( tan(2x) - sec(2x)) +c did I do something wrong ? 😭😭😭

[@aaravshah3843]

Uhh I converted the 2sinxcosx to sin(2x) and got a different answer… Is there something I’m missing? Am I not allowed to do that? 😭

[@mathwithprofessorv]

That’s ok…it’s what you did after that may be the issue…?

[@buzzybola]

What happened to ur trig integral vid?

[@mathwithprofessorv]

😂 I didn’t love it! I’m gonna redo it with one more example and maybe a dark background soon!