Question

integration
tan x dx

=

− ln | cos

x| +

C ;;inthis how to slove In​

Answer 1

$\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}$

⭐Actually welcome to the concept of the Integration,

⭐So by the substitution method we get as

⭐integration tanx dx = log(sec x) + C

Answer 2

$\bold {\huge {Answer :-}}$

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✭Integration✭

➛By method of Substitution

$I = \:\int\limits_{}^{}tanx. dx\\\Rightarrow\:I=\int\limits_{}^{}\frac{sinx}{cosx}dx\:\:\:\:[from\:Trigo.] \\\\let\:cosx\:= u\\differentiating \:both\:side\\\Rightarrow-sinx. dx= du\\\\putting\:in\:I\\\\\Rightarrow\:I = \:-\int\limits_{}^{}\frac{du}{u}\\\Rightarrow\:I= \:-log|u|+c\\\Rightarrow\:I = - log|cosx|+c$

$I = log (\frac{1}{cosx})+c$

$\bf\huge\boxed{\Rightarrow\:I= log(secx) +c}$

Or

$\bf\huge\boxed{\Rightarrow\:I= ln(secx) +c}$

Here, C is isorbitary constant

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