Integral of tan^2x

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This calculus tutorial will help you learn how to integrate tan^2(x) with a trigonometric identity. Remember we can divide sin^2(x)+cos^2(x)=1 by cos^2(x) and get the identity that tan^2(x)=sec^2(x)-1.

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#calculus #math #blackpenredpen #tutorial #college #apcalculus

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smokeypillow

This video was made while i was still learning simple long division and multiplication, now 8 years later i can watch this video and understand what is being done. Thank you blackpenredpen for making such good videos for this long!

koioioioi

Congratulations on solving this integral!
You are a great person, and your style is very smart and efficient.

robertoteixeira

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rawdawg

LOVE your videos indeed this was so fundamental building question besides that your way of interpreting is so good i hope everyone find fun in calculus ❤

UROOZFATIMA

I had struggled with this problem for 2 days, used u substitution, trig identity tan = sec^x-1, integration by parts but I couldn't progress. Then finally checked by your channel and boom, explanation took only about 2 minutes. It was so obvious that used improper identity for tan function. Thank you very much.

sardarbekomurbekov

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alisynrecchia

Why is this teacher so enjoyable to listen to?

johnx

you could also just +1 and -1, tan^2x+1 is sec^2x -1 and you reach the same spot

Commonstories-lzmk

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zazem

Without knowing this I wouldn't have been able to solve my problem which I had been for a long time, thanks😄

kamalakarpol

you speak so politely i love this so much math seems easier when you do it :)

HornOKPlease

Ik I'm a bit late, but why didn't you just add (+1-1) then you'll have to integrate (tan^2 +1) and (- 1)

khairihammami

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Thank you 😍

mohammednourinjerini

Love this video, it was very helpful with my maths revision!

tllinnr

U can change tan²x to sec²x -1 then integerate directly

mohamedmorsy

Thank you you save me from Total failure
Ora ti adorerò come una divinità

matteogrelli

1.) decomp into sin and cos
2.) Weierstrauss
3.) ???
4.) profit

maalikserebryakov

why wouldnt you just use the identity at the start?

tan^2(x) = sec^2(x) - 1

integral of sec^2(x) - 1 is tan(x) - x + C

alwaysdowhateversnext

We can rewrite (tan(x))^2 = 1+ (tan(x))^2 - 1 so the integral becomes tan(x) - x + c

No-name

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