Integration By Partial Fractions (irreducible quadratic factors)

Dear calculus 2 students. Here we have 3 integrals of rational functions and they all have an irreducible quadratic factor in the denominator.

0:00 dear calc 2 students!
0:08 Q1 integral of x^4/(x^2+9)
3:15 Q2 integral of a big rational function
10:47 Q3 integral of a "bigger" rational function

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[bos]

In Romania we don't use those methods, but i love how you present it!! I had once a chance to use one of your methods in class and my classmates were shocked ;)) keep on the great work, professor!!!! Many good whishes from Romania!!

[adonnis]

I made the incredible mistake of reading “Calc 2” at the beginning as “Algebra 2”. Wow was I confused the entire video

[alberteinstein]

You make me love Calculus even more than I already do 😁

[kormosmate]

Last time i had to integrate something like these, i had an x^2+1 as factor in the denominator. I thought "ehh let's try using the cover-up method with complex numbers"'. Turns out it still works! The result will be a complex number in the from a+bi, but it's expectable, since you're looking for two coefficients in the numerator. So a and b will actually be B and C int the partial fraction.

[LheannMichelleFlorento-xcux]

I like it of how he holds a Pokemon mic
😂

[wuyqrbt]

Hello teacher
If you don't like integral and parenthesis next to each other, you can use bracket instead of parenthesis!
Or ...or you can use fatter integral (integral with obesity!)
I love you teacher

[nimifhana]

Watched this video while doing homework and it was helpful, then on the exam l took today, this was the case and completely forgot what to do 😭😭😭 but your vids are helpful, thanks!

[KK-snct]

5:11 If you're here from the bloopers video

[janmejaypant]

Thanks.... was struggling with the same problem

[nemanjalazarevic]

I think for the first one trig sub works
x=3tan0
dx=3sec²0
tan⁴0/9sec²0 sec²0 d0
tan⁴0/9 d0
1/9 ×Integral(tan⁴0)
And then it gets absurd
(Integral of tan⁴0=tan³0/3 -tan0+x+C
=x³/3 +C
(I havent watched the video yet Im excited to see what he gets)

[wuyqrbt]

What about *as always: That's It* ❓❓

[Joseph]

I love the poster in the background! Where can I get one??

[chaos-c]

How you use 2 pens at once
And switch

[mohamedibrahim]

Guys do any one has a prove of quadratic denominators have linear numerator? And on the same rythme

[utkarshambasta]

Wrong Solution:
8*(4)²-10(4)-3= 144-40-3=101

[yazdan]

That pokeball he is holding throughout the video
Why?