integral of tan^2(x)*sec(x), calculus 2 tutorial

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integral of tan^2x*secx
integral of tan^2(x)*sec(x)

Steve Chow @ Los Angeles Pierce College
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Best way to attack this is to write the integral as //( tan x ) ( tan x sec x dx). Note that I use the double slash as the integral sign here. Then let tan x = u, (sec x)^2 dx = du and
tan x sec x dx = dv, with tan x = v. Then proceed with integration by parts ( //udv = uv - //v du ) and we have Integral = tan x sec x - // (sec x)^3 dx.
then we have
Integral = tan x sec x - // (sec x)( 1 + (tan x)^2) dx and
Integral = tan x sec x - // sec x dx - // sec x (tan x)^2 dx and proceeding ....
Integral = tan x sec x - ln (sec x + tan x ) - Integral
2 (Integral) = tan x sec x - ln (sec x + tan x) and
Integral = (1/2) ((tan x sec x) - ln (sec x + tan x)) + C
A most straight forward and time saving approach!

thomasarch

didnt have to check the other video for sec^3 because you eventually get
integral (tan^2x secx dx) = secxtanx - integral(tan^2xsecx)dx - ln (secx+tanx)
see, the two integrals match and its very easy from there. No need to look and find the integral of sec^3x.

syxgzzr

That was a very simple and concise explanation, great job dude. Very helpful!

anthonylatorre

you are a legend thank you for this skinny math king

saraht

The video seemed promising.. 4 minutes - not bad at all. Reality: The amount of work that needs to be given if we want to solve it including the solution of integrals of sec^3x and secx is incredible :D

FF-wloo

I'm so lucky to have found this channel. Thanks!!!

skyrat

2:19 "very easy".

Me: do you want me to punch you in the face? lol

2:20: ohh, he was talking about the video

flaviarosadeandrade

应该证一下sec^3x的积分这样才比较完整因为教材上直接提供的只是secx的积分

hrujqwk

Hablo español y su acento se escucha bien gracioso 😂😂😂😂

miriamo

where did the 1/2 for the integral of sec^3(x) come from????

KristellaJackson

Question: who else came here after seeing a post in insta?

amoonomar

Thank you very much sir. I got stuck on this one. Integrate tan^2(x)sin^4(x). May you help

mygoal

So to solve this problem, i need to watch three videos? I dont know what you mustve been thinking or if you are flat out lazy. Instead of integrating it by parts you rather have your views click links. Anyone that is about to watch this, dont, its just a waste of your time.

kevinnijjar

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