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Evaluate the following integration ...

Evaluate the following integration
`int tan x tan 2x tan 3x dx`

Text Solution

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`tan 3x=(tan2x +tanx)/(1-tan2xtanx)`
` :. tan3x tan2x tanx=tan3x -tan2x -tanx`
` :. int(tan3x-tan2x-tan x)dx`
`= -(1)/(3)log|cos 3x|+(1)/(2)log|cos 2x|+log|cos x|+c`
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