Tan x'in İntegrali Nedir ?
Tan x'in integrali, -ln |cos x| veya ln |sec x|'tir.
∫tan x dx=−ln ∣cos x∣+c=ln ∣sec x∣+c
Tan x'in İntegralini Bulma
∫tan x dx=?
tan x=cos xsin x
∫tan x dx=∫cos xsin x dx
cos x=u
d (cos x)=du
(cos x)′ dx=du
(cos x)′=−sin x
−sin x dx=du
sin x dx=−du
∫tan x dx=∫u−du
∫tan x dx=−∫udu
∫xdx=ln ∣x∣+c
∫tan x dx=−ln ∣u∣+c
∫tan x dx=−ln ∣cos x∣+c
∫tan x dx=ln ∣cos−1 x∣+c
∫tan x dx=ln ∣cos x1∣+c
sec x=cos x1
∫tan x dx=ln ∣sec x∣+c