What is the definite integral `int_(0)^pi 3*tan x dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The definite integral `int_(0)^pi 3*tan x dx` has to be determined.

`int_(0)^pi 3*tan x dx`

=> `3*int_(0)^pi sin x/cos x dx`

let `cos x = y`

`dy = -sin x*dx`

=> `-3*int_(0)^pi (1/y) dy`

=> `-3*ln cos x` between 0 and pi

=> `-3*ln cos pi + 3*ln cos 0`

But `ln cos pi` is not defined as the logarithm of negative numbers is not defined.

The integral `int_(0)^pi 3*tan x dx` is not defined.

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