Tan x'in İntegrali

Tan x'in İntegrali Nedir ?

Tan x'in integrali, -ln |cos x| veya ln |sec x|'tir.

$\int tanxdx=-ln|cosx|+c=ln|secx|+c$

Tan x'in İntegralini Bulma

$\int tanxdx=?$

$\boxed{tanx=\frac{sinx}{cosx}}$

$\int tanxdx=\int \frac{sinx}{cosx}dx$

$cosx=u$

$d(cosx)=du$

$(cosx{)}^{\prime }dx=du$

$\boxed{(cosx{)}^{\prime }=-sinx}$

$-sinxdx=du$

$sinxdx=-du$

$\int tanxdx=\int \frac{-du}{u}$

$\int tanxdx=-\int \frac{du}{u}$

$\boxed{\int \frac{dx}{x}=ln|x|+c}$

$\int tanxdx=-ln|u|+c$

$\int tanxdx=-ln|cosx|+c$

$\int tanxdx=ln|co{s}^{-1}x|+c$

$\int tanxdx=ln|\frac{1}{cosx}|+c$

$\boxed{secx=\frac{1}{cosx}}$

$\int tanxdx=ln|secx|+c$