Question

integral of tanx tan2x tan3x dx=​

Answer 1

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Answer 2

Given:

The expression tanx tan2x tan3x

To find:

Integral of tanx tan2x tan3x dx

Solution:

From given, we have,

The expression is tan x tan 2x tan 3x

tan x tan 2x tan 3x = tan 3x - tan 2x - tan x

∫ (tan x tan 2x tan 3x ) = ∫ (tan 3x - tan 2x - tan x)

= ∫ tan 3x dx - ∫ tan 2x dx - ∫ tan x dx

= 1/3 log (sec 3x) - 1/2 log (sec 2x) - 1 log (sec x)

∴ ∫ (tan x tan 2x tan 3x ) = 1/3 log (sec 3x) - 1/2 log (sec 2x) - 1 log (sec x) + c