Integral of the Day 6.16.24 | Semi-Spicy Trig Integral with some Slick Tricks! Math with Professor V

Here's a trig integral that really required some clever tricks and determination! Did you solve it differently? I'm curious if there's a more succinct and elegant solution. Let me know in the comments below! :) Thank you all for your continued support, it means the world to me!
Here's the video on the Weierstrass substitution of t=tan(x/2):
• Substituting t=tan(x/2...
Don't forget to LIKE, Comment, & Subscribe!
xoxo,
Professor V
linktr.ee/mathwithprofessorv
Shop my Merch: math-with-professor-v.mysprea...
Calculus 2 Lecture Videos on Integration:
Integration by parts: • Calculus 2: Integratio...
Tabular Integration: • Integration by Parts -...
Trigonometric integrals: • Calculus 2: Trigonomet...
Trigonometric Substitution: • Calculus 2: Trigonomet...
Partial Fraction Decomposition: • Calculus 2: Integratio...
Strategy for Integration: • Calculus 2: Strategy f...
Improper Integrals: • Calculus 2: Improper I...
Trig Review:
Unit Circle: • Trigonometry: Circular...
Trig Identities: • Precalculus: Trigonome...
Sum and Difference Formulas: • Precalculus: Sum and D...
Double Angle & Half-Angle Formulas: • Precalculus: The Doubl...
Calculus 3 Video Lectures:
• Calculus 3 Video Lectures
#mathwithprofessorv #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos #integrationbyparts #integralcalculus
Join this channel to get access to perks:
/ @mathwithprofessorv
Socials:
IG: @mathwithprofessorv
TikTok: @mathwithprofessorv
I'm also an Amazon influencer, so feel free to support and shop:
amazon.com/shop/mathwithprofe...
EXCITING NEWS: You can now sign up for my Patreon at the link below!
/ mathwithprofessorv
My Patreon is a place for students to have access to exclusive ad-free content not available on my UA-cam channel! Access to the library of additional videos, worksheets, and more is available with the "Star Pupil Package" tier for just $9.99/month (USD).
/ mathwithprofessorv
This video is copy protected and cannot be downloaded or used in any capacity without my permission.

[@benriakchangdar4963]

I liked it.

[@Algebrainiac]

I couldn’t do this LOL 😂 you find the craziest integral problems!! Woooo they’re hard LOL. As always great job ❤

[@mathwithprofessorv]

This one was extra spicy!!!! 🌶️ 🥵 Haha great job, and I’ll do a more mild one next! Every now and then it’s fun to spice things up 😉

[@isaacfielsted37]

Outstanding example

[@mathwithprofessorv]

Thank you! ☺️

[@tony413chow]

Thanks for letting me know to multiply sine(theta).

[@mathwithprofessorv]

Happy to help ☺️

[@Algebrainiac]

I multiplied sin(θ) of course not illegally. Lol I multiplied it on top and bottom. I did that as my first step and so then I got integral of
Sin(θ)/sin²(θ)cos(2θ)
And then I made the bottom into terms of cosine
So I got
sin(θ)/(1-cos²(θ))(2cos²(θ)-1)
Then I made u=cos(θ) and then du=-sin(θ) dθ
So I got
- integral(-du/[(1-u²)(2u²-1)])
And then that’s where I got lost because I don’t know how to do partial fractions with quadratic factors at the bottom LOL

[@mathwithprofessorv]

That’s really great!!!! 👍🏻 I think figuring out the substitution in the beginning was pretty tricky, be proud of yourself! ☺️☺️☺️

[@Algebrainiac]

@@mathwithprofessorv thank you 🥰