Trigonometric Integrals - Part 4 of 6

[BrothaDavid]

Dammit, I don't care if you're a Mormon or not, just let me watch Patrick. Go away.

[Angelgrrl04]

@1:57 - It said to save tanxsecx, and use tan^2x=sec^2x-1 to replace it. Yet you replaced tan^2x with sec^2x-1. Your first three videos you used what you save and replaced it with. But in this one, you just replaced the tan^2x. Why is that?

[redrum41987]

I'm blowin thru these now, thank you

[jaleed]

for tan^5x, can we change it to sin^5x/cos^5x, and intergate. Will it be the same answer

[patrickJMT]

@jaleed well, after you change it, how do you integrate it?

[jaleed]

@patrickJMT Strip out a sin, and replace sin^4x with the identity sin^2x=1-cos^2x. Use u sub to take out the stripped sin. and then intergate?

[erikaalysse]

@jaleed you would do u-substitution and let cosx = u,

[gangstak3d]

Hi patrick, i'm really srry fr asking you dis ques. Infact i don't think u'll even answer but can you plz simplify the rules of trigonometric integration for me please. You have 6 vids and i watched all of them, they're a big jumble in my head. For e.g you said tan^n(x)*sec^m(x) nd if n is odd u save secxtanx but what about m?. Can you please clarify this or make another vid really soon that talks about both exponents (for cos and sin aswell). I hope you dont mind this lenghty ques, thnx alot!!!

[megangs93]

I think it is the integral of tanx is ln cos x....

[swabsDE]

if i get a B or better on my calc final tomorrow I'm sending you money, you deserve it more than my professor...

[da1booger13]

Hmmm, patrick, at 7:20, shouldn't there be a 1/secx there? I say this because of when the 'u' was taken to equal secx. In that case, only the tanx would have remained in the integrand. Thus, when taking the derivative of the u value(secx) which equals 'secxtanx', that derivative would have only crossed out the tanx in the integrand. So it would seem to leave you with a 1/secx. Anyway, I might be brutally wrong, please take me in the right direction if so.

[patrickJMT]

@da1booger13 you are probably right, i am too lazy to rewatch

[NguyenEmpir3]

0:08-0:20

Even a great mathematician like Patrick gets tongue twist. lol.

[hehey90]

you are an amazing person

[forkerstone]

Only patrickJMT's terms can hang out.

[raceltot]

@beshjm this topic also drives me crazy o.o

[christinajl]

The integral of tan(x) is: -ln(cosx)+C , isn't it? I didn't quite catch why is the ln(secx)+C...

[Miguel11adjr]

@christinajl you can use the ln properties, -ln(cosx) = ln(cos^(-1)x) = ln(secx)

[christinajl]

@Miguel11adjr Thank you!

[mush352]

in the second question ,i do not get why u didnt let u=secx then du=tanx...then it would be S (u^2-1)du= (u^3)/3+u+c

[SimcaLux]

@mush352 because if u=secx, then du would be secxtanx

[pumitaproductions]

0:40 i thought you fell and died lol

[isidbigi]

'cookie cutter?? Nigga I find this difficult but still an amazing tutorial video. Keep up the good, I will but ur app to show my appreciation

[shweterpatron]

YOU ARE AWESOME

<3333

[ricanhurdler]

U^4/4 does the +C not tag along? why not?

[rezwan739]

Thanks alot man... got an exam tomorrow your videos helped lot as a last minute preparation.

[drksnix]

Solve sqrt(tanx)

[The3jji]

Can I send you an e-mail... I'm trying to post my solution as a comment, but for some reason it says Error.

It says that we should be friends?

[The3jji]

I'm having another solution O.O

[RedTearS88]

i have midterm tomorrow.

I was trying to understand from my book with no use !

after looking at ur videos i believe i will do good =D

thanks for all your help and time. ( ur the best )

[watsongenetics]

If you split intgeral tanxsec^2x into tanxsecxsecx, cant you use a v=secx substitution, making the answer (sec^4x)/4 - sec^2x + ln|secx| + C ?

and btw THANK YOU SOOOOOOOOOOOO MUCH, your videos are the only reason I'm passing Calculus right now!

[Smarkand28]

thx this is rly helping my ap calc

[dissolutionman]

You're the best, man. I'm In a six-week Calculus II course and this really helps clear up what can be a rushed and confusing lecture. Thanks for this.

[Labr1283]

THANKS DUDE!!!!!

[jarjarin]

is teaching your real career? if so, i bet you make a good and well-liked teacher! ;D

[OffAnon]

i did this different then any of the comments i saw and was wondering if it was correct: tan^5xdx -> tan^2xtan^2xtanxdx -> (sec^2x-1)tan^2xtanxdx u=x du = sec^2xdx expand out the sec^2x-1 sec^2xtan^2x-tanx - (new integrand) tan^2xtanxdx u^3du - (integrand) (sec^2x-1)tanxdx u^3du - (integrand) sec^2xtanxdx-(integrand)tanxdx u^3du-(integrand) udu - (integrand) tanxdx answer: 1/4(u^4) - 1/2(u^2) - ln|secx| + c sub u in: 1/4tan^4x - 1/2 tan^2x - ln|secx|  + c

[elementoxygen]

This was an awesome vid. I have one thing to say though. You for to put dx on the du part that was equal to ∫secx*tanx

But It was still a great vid!!!

[ZzFactorzZ]

when you integrate sec^4x * tanx

can't you break it down to

sec^2 (x) * sec^2 (x) * tan x

then if u substitute sec^2 (x) into

1+ tan^2 (x)

let u=tanx etc.

does that work too??

[mjk2492]

Seriously, I love you man.

[bilnemer]

Em, I thought what if n was even and m odd? Ho can we solve it?

[bilnemer]

Hey, Patrick, that amazing =D

Even if I may find a little bit slow, you really don't skip steps, and that's good for everyone. Keep up, that's good work !

[arabiangurl08]

amazing! thank u!

[djspmix]

final tomorrow and this makes it so much easier!!!

[usamaaftab80]

yes! it is also correct! integral of tan u can be

ln|sec u|+c as well as -ln|cos u|+c

[deeds1970]

My integral sheet says... int(Tan u) = -ln abs(cos u) + c.

Is this incorrect?

[aim9x]

yes, by logarithmic property, you can think of it as ln abs( (cos u)^ (- 1) ) +c)

therefore it becomes ln abs(sec u) + c

[mangina0mmm]

@deeds1970 you are right

[Tubbs2Cool100]

@deeds1970 yup it is, it is the same thing as what patrick did

using log rules: ln(secx) = ln(cosx)^ -1  = -ln(cosx)

so when you integrate tanx you can get both of these answers, they're just in different forms.

[joelgdz]

@deeds1970 . it is correct because -ln(x)=ln(1/x)

the negative just flips whatever is on the inside.

[beshjm]

awesome, i just finished th 6 parts, will go to the exam in one hour and this part (trig integral subs) drove me crazy, but not anymore ;)

[patrickJMT]

excellent : )

[syriankid4ever]

Thanks a lot.

[bnssapp]

hi..i have a question again..

why did you u-subs so late???

look at 4:52, if you let u=sec(x) and du=tan(x)sec(x)dx, you will end up with something like this:

sec^4(x)/4 - sec^2(x) + ln |sec(x)| + C

[tony225]

bnssap: one thing you have to notice about Patrick is he is very methodical. He doesn't skip steps that you may find yourself skipping once you get good at the technique.

If he did the substitution at the point you suggest it might be confusing to some viewers because he hadn't yet "broken off" a sec(x) that you'd need to form your du.

He just did the extra steps so it is clear that you end up with a sec(x)tan(x) so you can do your u-sub.

[hbquanie]

IMPORTANT QUESTION: at the end of the video, why did you make v=something....instead of just sub in u=......?? I have seen all ur other videos, and i fully understand the rules....but, in this case, what do i do? thanks

[k0fdark]

u = something its the same than

v= something and its the same than

w= something

z= something

in fact you can use any variable for subtitution, same idea

[hbquanie]

thats not what i meant....watch the end of the video....sub in u or v is not the same thing!..u will get a different answer.

[bnssapp]

i think its just another variable..you can use any letter u want

[tony225]

He breaks the integral up into three separate integrals and uses a different "u" in two of them, so he just calls one of them v to avoid confusion.

[phnxme7]

Wow! U r the best teacher ever!!..

Great tutorials..!!..

Wish I could learn under you, but i'd havta fly over to attend your lectures.. :)

Anyways, my question is in the last part of the solution in the 2nd problem wherein:

[robbydamusicman]

FOR ONCE IN MY LIFE I"M GETTING IT!!! I'm getting it before u even show it

[isoman2kx]

Hi Pat. Great video overall!

Just a few comments/suggestions.

(1) When you start out with the formulas in the beginning , you use M and N on the left side and A & B on the right side. This was slightly confusing until I looked at the formula in my book that had m and n on both sides.

(2) The annotation at 3:21 doesn't include the 10, it just says "1 / "

Keep up the good work!

-Travis

[poonangnang]

where have you been all my life

[granadaza]

great again

[siloam483]

im sorry i see someone else already made a comment about the integral of tanx. i dont understand how they both are correct. if you could explain that would help me alot. thanks. and thanks for all your videos very very helpful

[patrickJMT]

SkipiXX (1 week ago)

(secx)^2 = (tanx)^2 + 1. So the results differ only by constant (C) value. Your result is also correct...

[siloam483]

shouldnt the integral of tan x = -ln absolute value of cos x

[lemonane111]

When you integrated (secx)^2(tanx), I paused and tried it myself. I had v = secx and dv = secxtanx instead. I substituted v back in after I was done, and I ended with (secx)^2 which definetly does not = (tanx)^2. What went wrong?

[SkipiXX]

(secx)^2 = (tanx)^2 + 1. So the results differ only by constant (C) value. Your result is also correct...

[lemonane111]

thanx, my calc teacher explained it just the other day.

[ziolp]

wow, that is really long at step 4 (4th = sign)

[bordenw]

I want to apoligize, I see how both answers are the same thank you.

[patrickJMT]

no problem!

[bordenw]

your answer is wrong. The antideverivate of tanx is -ln(cosx).

[patrickJMT]

my answer is not wrong.

neither is yours.

[shortcut411]

thanks!!

this helped me!!

[Syruscleat]

Splendid demonstration of trig integration and substitution. Encore!