Question

what is the integral of tanx

Answer 1

i see on a lot of math sites that say its ln secx and others that say -ln cosx

Answer 2

hint: tan(x) = sin(x)/cos(x)

use u-substitution and let u = cos(x)

Answer 3

when is it ln secx?

Answer 4

the two are equivalent (just different ways to express the same thing)

Answer 5

so either one i use i will still get the same right answer

Answer 6

\[\Large -1\ln(\cos(x)) = \ln((\cos(x))^{-1})\]

\[\Large -1\ln(\cos(x)) = \ln\left(\frac{1}{\cos(x)^{1}}\right)\]

\[\Large -1\ln(\cos(x)) = \ln\left(\frac{1}{\cos(x)}\right)\]

\[\Large -1\ln(\cos(x)) = \ln\left(\sec(x)\right)\]

Answer 7

okay thank you for clearing it up

Answer 8

no problem