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How to integrate log (1+tan (x)) from 0 to π ? Is the function even or odd or neither?

How to integrate log (1+tan (x)) from 0 to π ? Is the function even or odd or neither?

Grade:12th pass

1 Answers

Nandana
110 Points
7 years ago
this below fig. shows the integration which we want
Image result for integrate tanx from 0 to pi graph
 as we can see that , this integration is not converging it goes to infinite
we can show it by doing integration also
let’s take ∫0pi (1+tan x) dx = ∫0pi  dx + ∫0pi tan x dx = π + ∫0pi sin x / cos x dx
= π + mod(∫01  1/ u du) +mod ( ∫-10 1/ u du)  [ take u= cos x , then
du = -sinx dx ] 
= π + ln (0)+ ln(0) →  infinite
and it is neither even nor odd in this intervel as we can see .
Thank you .

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