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∫(\tan x)⋅dx

$I:=∫\limits_{0}^{x} (\tan x)⋅dx=?$

$s:=\cos x$

$ds=-(\sin x)⋅dx$

$÷{ds}{-(\sin x)}=dx$

$I=∫÷{\sin x}{\cos x}⋅dx$

$I=∫÷{\sin x}{\cos x}⋅÷{ds}{-(\sin x)}$

$I=∫÷{ds}{-(\cos x)}$

$I=-\ln|s|$

$I=-\ln|\cos x|$

Author: Danny (remove the ".nospam" to send)

Last modification on: Sat, 04 May 2024 .