First slide

Methods of integration

Question

$\int \cot x \cot (240^{0} - x) \cot (240^{0} + x) d x$

Moderate

A

$\frac{- 1}{3} \log (\sin 3 x) + c$
B

$\frac{1}{3} \log (\sin 3 x)$
C

$\frac{1}{3} \log (\sin 3 x) + C$
D

$\frac{1}{3} \log (\cos e c 3 x)$

Solution

We know that
$\begin{array}{l} \tan x \tan (240^{\circ} - x) \tan (240^{\circ} + x) \\ = \tan 3 x \\ \int \cot x \cot (240 - x) \cot (240 + x) d x \\ = \int \cot 3 x d x \\ = \frac{1}{3} \log (\sin 3 x) + C \end{array}$

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