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Problem If ∫ 3 cot 3 x − cot x tan x − 3 tan 3 x d x = p f ( x ) + q g ( x ) + c \int \frac{3\cot 3x-\cot x}{\tan x-3\tan 3x}\,dx=p\,f(x)+q\,g(x)+c ∫ t a n x − 3 t a n 3 x 3 c o t 3 x − c o t x d x = p f ( x ) + q g ( x ) + c c c c p = 1 ; q = 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 − tan x 3 + tan x ∣ p=1;\ q=\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}-\tan x}{\sqrt{3}+\tan x}\right| p = 1 ; q = 3 1 ; f ( x ) = x ; g ( x ) = ln 3 + t a n x 3 − t a n x p = 1 ; q = − 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 − tan x 3 + tan x ∣ p=1;\ q=-\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}-\tan x}{\sqrt{3}+\tan x}\right| p = 1 ; q = − 3 1 ; f ( x ) = x ; g ( x ) = ln 3 + t a n x 3 − t a n x p = 1 ; q = 2 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 + tan x 3 − tan x ∣ p=1;\ q=\frac{2}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right| p = 1 ; q = 3 2 ; f ( x ) = x ; g ( x ) = ln 3 − t a n x 3 + t a n x p = 1 ; q = − 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 + tan x 3 − tan x ∣ p=1;\ q=-\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right| p = 1 ; q = − 3 1 ; f ( x ) = x ; g ( x ) = ln 3 − t a n x 3 + t a n x p = 1 ; q = 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 − tan x 3 + tan x ∣ p=1;\ q=\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}-\tan x}{\sqrt{3}+\tan x}\right| p = 1 ; q = 3 1 ; f ( x ) = x ; g ( x ) = ln 3 + t a n x 3 − t a n x p = 1 ; q = − 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 − tan x 3 + tan x ∣ p=1;\ q=-\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}-\tan x}{\sqrt{3}+\tan x}\right| p = 1 ; q = − 3 1 ; f ( x ) = x ; g ( x ) = ln 3 + t a n x 3 − t a n x p = 1 ; q = 2 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 + tan x 3 − tan x ∣ p=1;\ q=\frac{2}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right| p = 1 ; q = 3 2 ; f ( x ) = x ; g ( x ) = ln 3 − t a n x 3 + t a n x p = 1 ; q = − 1 3 ; f ( x ) = x ; g ( x ) = ln ∣ 3 + tan x 3 − tan x ∣ p=1;\ q=-\frac{1}{\sqrt{3}};\ f(x)=x;\ g(x)=\ln\left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right| p = 1 ; q = − 3 1 ; f ( x ) = x ; g ( x ) = ln 3 − t a n x 3 + t a n x Browse the problem library