Integral of tan(x)*sec^3(x), tan sec approach, calculus 2 tutorial

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Integral of tan(x)*sec^3(x), tan sec approach

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Комментарии
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This guy explains everything straight forward.

martinalmaraz
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Thank you so much! I love you, you are the best!

gilmaferrer
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Professor, I just wanted to make a point pertaining to how much different our styles of integration are, we both arive at correct results, but use very different approaches. E.g. I would have first rewritten the integrand as sin(x)/cos^4(x) and done a t substitution t=cos(x) which would result with an integral easily solvable via the power rule. Also, thanks for widening my views in integration and math in general, your videos are the best!

mrkenzivedran
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Thank you for finally explaining where that power went. All the help I could find would leave that out with no explanation and I just wanted to know WHY! Seems obvious now, lol, but hindsight is 20/20. Subscribed, you earned it!

matthewwells
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I personally change that integral to sinx/cos^4x dx and using u subtitusion u=cosx...

ahmadyogi
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Sir, you're a math-magician and thank you for this video.

calyptracatochrysops
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saved me from crying on a Friday night thanks man

neilsmit
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Thank you so much!! This really helped me a lot.

andreac.
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Thanx sir i'm from india and you
you lecture is most useful 👌🏿👌🏿👌🏿

AmirAkela
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I LOVE YOU
nobody else can explain me that

tatianasanchezphillips
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Fue mas fácil de lo que parece, mil gracias <3

paokogane
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Y si separó sec^2 x tan x sec x, y convierto a tangente el sec x, puedo usar u= tan x du= sec^2?

ChristoSantos
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why didn't you substitute both sec for U. shouldn't it have been tanx U U^2?

clearilluion
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Integral = (secx)^2 d(secx) = 1/3(secx)^3 + C, so we forget “the U business”

seegeeaye
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so in this problem u=sec(x) but we aren't forced to replace all instances of sec(x) with u?

In another problem I did, integral of (sin(x))^7 * (cos(x))^5, in one of the steps I made u=sin(x) and then replaced all instances of sin(x) with u. My final answer ended up being right.

So then are we able to use u in both ways? Where it can replace one instance OR all instances freely? Or did I just coincidentally end up with the correct answer in my problem?

TheSilverWolf
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just take ( U=sec x) and then solve it will give result in 2

inclinedscorpio
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No entendí lo que estaba diciendo pero sí el ejemplo en la pizarra:)

mariafernandatorresbarron
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how to solve integral of tan^4xsec^3xdx I neeed immediately 🙁🙁🙁

dhasarathi
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I am watching this after 6 years now in June 2021. And I feel like the teacher should have kept the mic down while explaining. Thank you for explaining, I got it!

omkarpol