The Integral of (1-tanx)/(1+tanx)

Evaluating the indefinite integral of (1-tan(x))/(1+tan(x))

[@PackSciences]

You can remove the abs() : the result can be written as ln(abs(cos(x)+sin(x))) = (1/2)* ln((cos(x)+sin(x))^2) = (1/2)* ln(1+cos(x)sin(x)) = (1/2)* ln(1+sin(2x)/2) and obviously + C

[@saddamhussain-sb2qd]

Thanks a lot,I had watched 3 videos for the same question but none of them said clearly that they are converting into (1/u)du. Heart fully thanks a lot

[@gameplace2]

Thank you so much.

[@ATULAA_2110]

How should i solve this que without cos n sin by π/4 -x

[@paintnsketch2136]

Not lazy anymore ❤️
Brought some interest

[@fabriziofernandes4365]

Nice!

[@lebinh7052]

from vietnam and thanks a lot :D

[@rufinajoe6338]

Thank you sir 😊

[@user-rt9gz2vd8i]

Thank you from Japan 🇯🇵

[@AsThEtIcViBe01]

Thanks a lotttt

[@walterbaldemor2128]

Thanks it helped me

[@geniuscreations8711]

Thanks

[@user-ace96plays]

thanks

[@uditkumardhankar4891]

Can u solve for 1+tanx/tanx-2

[@raushanisonline]

defferentiate this 1/(1+tan^3x)^2

[@boardexams4563]

Lol , theres a formula for this . 1-tanx/1+tan = tan(pi/4 -x). Boom , its done

[@hariommeena7877]

why can't we solve it by rationalization ?

[@boardexams4563]

Hariom Meena theres no use of rationalization . It will just become harder because there is no formula for 1-tan^2x. If it was 1+tan^2x , you could have replaced it with sec^2x .

[@mohdzaid4719]

Lol met bolo because you couldn't find same ans by converting tan(pi/4-x)

[@dontony3514]

U won't get answer in this eternity 😂

[@greshambasnet7553]

How can we further solve it to lncos(45-x)?

[@gautamdoshi9168]

yes i have same doubt

[@bablisingh8171]

Can you solve 1/1-cotx

[@surendhramusic1680]

Tqq so much sir

[@samhita12m]

very nice

[@kidspinocchio2230]

Thanks video

[@raushanisonline]

NYC

[@sk7855]

what if we do it by putting tan(45-x) ??

[@fazilshirazi1451]

bro that is for 1+tanx /1-tanx...but it is 1-tanx /1+tanx

[@sk7855]

@@fazilshirazi1451 BRO WHAT DO U WANT TO SAY I DIDN'T GET ; PLS SEE THE QUES CAREFULLY

[@ayushagrawal264]

Waah👍

[@General12th]

But... but... what happens if you forget the constant of integration?

[@TheLazyEngineer]

try it on your next exam, and report back here

[@General12th]

Just tried it.
Failed the test. Removed from class. Kicked out of college. Arrested for crimes against mathematics. Now I'm writing to you from death row. THANKS A LOT! >:(

[@fabriziofernandes4365]

J.J. Shank lol

[@gusmoraless]

you can write it too as: (1/2)ln|1+tanx| + C

[@fleurdelacour5247]

How the 1/2 come out?

[@gusmoraless]

@@fleurdelacour5247 I made a mistake.. If you factored out cos(x) and change it to sec(x) = sqrt[1+tan²(x)], I THOUGHT, it would yields a simplified expression... But no.

[@fleurdelacour5247]

@@gusmoraless Yeah if it were 1+tan^2 I think that would have been the result but as it has no square it should be the answer of the vid 💀

[@santhameera2559]

2023 class 12 boards set 2 first qn 😢

[@torsha1384]

integration((10^x)-1)/((10^x)+1) dx

[@SRNSHRDDY]

Bruh should we not rationalise denominator ?

[@KapilBodhare15]

Please need solution for integral 0 to pi/4 ((1+tanx)/(1-tanx))... Please tell me the steps also

[@TheLazyEngineer]

follow a similar logic as in this vid

[@darkemperor9006]

A very easy question but couldn't guess the next step.
Very surprised to see both Cymath and photomath couldn't solve it.