Integral of tan^3x*sec^4x (read pinned comment)

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integral of tan^3(x)*sec^4(x), calculus 2 tutorial
trig integral, trigonometric integrals

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#blackpenredpen #math #calculus #apcalculus

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It's also possible to do it this way:
Integral of (tan^3(x)*sec^2(x))* sec^2(x) dx
Then use sec^2(x)=tan^2(x)+1 and we get
Integral of (tan^3(x)*(tan^2(x)+1))* sec^2(x) dx
And We can do u-sub from here by letting u = tan(x)

blackpenredpen

I feel like this YouTuber is one of the most reliable online supports out there in terms of learning calculus (Paul's online math notes is also super helpful). He is very clear and very positive - a great natural teacher and really smart of course. Good work!

mattmitchell

You make it look so easy. Thanks a lot

armandosanchez

"...into the U world" I like that - it's a neat way of thinking about it. :)

Ensign_Cthulhu

Thaks for that explaination, real helpful . Regards from Colombia

LeucTequia

Thanks, man! Excellent layout of the video, btw.

jethro

Thanks sir, u make integral looks easier😭👍🏻👍🏻👍🏻

devianis

Integral of ((secx)^2 – 1)(secx)^3 d(secx) = 1/6(secx(^6 – 1/4(secx)^4 + C,
so forget the “U business”

seegeeaye

gracias, fué de mucha ayuda tu video...

luiseduardoortiz

Integrand=sin^3(x)/cos^7(x), then use t=tan(x/2), this would easily work

mrkenzivedran

obrigado mano, vc sempre me salvando rsrs

jorleandersonmaia

bro, why not call sec^2 (x) = tan^2 (x) + 1 ? So it should be: integral of tan^3 (x)*(tan^2 (x) + 1)* sec^2 (x)
after that we have: integral of (tan^5 (x) + tan^3 (x))* sec^2 (x).. calling u= tan (x) so dx=du/sec^2 (x).. cancelling sec^2 (x) we have..
integral of (u^5 +u^3) = tan^6/6 + tan^4/4.. but i tried putting values on the calculator and it doesnt work. Why ??

rogermilla