Mathematics

Solve:
$$\int { \tan { x } \tan { 2x } \tan { 3xdx }  }$$


SOLUTION
$$\displaystyle\int \tan x\tan 2x\tan 3x dx$$.
$$\tan 3x=\tan (x+2x)=\dfrac{\tan +\tan 2x}{1-\tan x\tan 2x}$$
$$\tan 3x(1-\tan x\tan 2x)=\tan x+\tan 2x$$
$$\tan 3x-\tan x-\tan 2x=\tan x\tan 2x\tan 3x$$
$$\displaystyle\int \tan 3x-\tan x-\tan 2x dx$$
$$\Rightarrow \dfrac{1}{3}log|\sec 3x|-\dfrac{1}{2}log|\sec 2x|-log|\sec x|+C$$.
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Subjective Medium Published on 17th 09, 2020
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