Is this :$int_-1^1exp (-tanh^-1 (x))dx=pi$ a well known integral representation for $pi $?

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I have tried to get interesting integral for interesting transcendental number , I have got the following :$int_-1^1exp (-tanh^-1 (x))dx=pi$ , really I didn't accross that integral in the web as shown here, Now I ask if the titled integral is a well known integral representation or no , And how i can evaluate that ?

integration pi transcendental-numbers

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edited Jul 21 at 4:16

Abcd

2,3761624

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

add a comment | 

up vote
0
down vote

favorite

I have tried to get interesting integral for interesting transcendental number , I have got the following :$int_-1^1exp (-tanh^-1 (x))dx=pi$ , really I didn't accross that integral in the web as shown here, Now I ask if the titled integral is a well known integral representation or no , And how i can evaluate that ?

integration pi transcendental-numbers

share|cite|improve this question

edited Jul 21 at 4:16

Abcd

2,3761624

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I have tried to get interesting integral for interesting transcendental number , I have got the following :$int_-1^1exp (-tanh^-1 (x))dx=pi$ , really I didn't accross that integral in the web as shown here, Now I ask if the titled integral is a well known integral representation or no , And how i can evaluate that ?

integration pi transcendental-numbers

share|cite|improve this question

edited Jul 21 at 4:16

Abcd

2,3761624

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

I have tried to get interesting integral for interesting transcendental number , I have got the following :$int_-1^1exp (-tanh^-1 (x))dx=pi$ , really I didn't accross that integral in the web as shown here, Now I ask if the titled integral is a well known integral representation or no , And how i can evaluate that ?

integration pi transcendental-numbers

share|cite|improve this question

edited Jul 21 at 4:16

Abcd

2,3761624

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

share|cite|improve this question

share|cite|improve this question

edited Jul 21 at 4:16

Abcd

2,3761624

edited Jul 21 at 4:16

Abcd

2,3761624

edited Jul 21 at 4:16

Abcd

2,3761624

2,3761624

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

asked Jul 21 at 2:22

zeraoulia rafik

2,1231823

2,1231823

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
1
down vote

Hint:
$$tanh ^-1left( x right)=frac12ln frac1+x1-x$$
check this link

share|cite|improve this answer

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

• 
  
  
  

  
  

  
  
  
  
  
  

  
  you are right, probably it is a simplification for well known integral representations of pi
  – zeraoulia rafik
  Jul 21 at 2:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  indded see the link in the answer
  – user577488
  Jul 21 at 2:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
  – zeraoulia rafik
  Jul 21 at 2:44
  
  

  
  
  
  

add a comment | 

Your Answer

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

Hint:
$$tanh ^-1left( x right)=frac12ln frac1+x1-x$$
check this link

share|cite|improve this answer

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

• 
  
  
  

  
  

  
  
  
  
  
  

  
  you are right, probably it is a simplification for well known integral representations of pi
  – zeraoulia rafik
  Jul 21 at 2:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  indded see the link in the answer
  – user577488
  Jul 21 at 2:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
  – zeraoulia rafik
  Jul 21 at 2:44
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

Hint:
$$tanh ^-1left( x right)=frac12ln frac1+x1-x$$
check this link

share|cite|improve this answer

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

• 
  
  
  

  
  

  
  
  
  
  
  

  
  you are right, probably it is a simplification for well known integral representations of pi
  – zeraoulia rafik
  Jul 21 at 2:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  indded see the link in the answer
  – user577488
  Jul 21 at 2:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
  – zeraoulia rafik
  Jul 21 at 2:44
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

up vote
1
down vote

Hint:
$$tanh ^-1left( x right)=frac12ln frac1+x1-x$$
check this link

share|cite|improve this answer

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

Hint:
$$tanh ^-1left( x right)=frac12ln frac1+x1-x$$
check this link

share|cite|improve this answer

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

share|cite|improve this answer

share|cite|improve this answer

edited Jul 21 at 2:36

edited Jul 21 at 2:36

edited Jul 21 at 2:36

answered Jul 21 at 2:29

user577488

1085

answered Jul 21 at 2:29

user577488

1085

answered Jul 21 at 2:29

user577488

1085

1085

• 
  
  
  

  
  

  
  
  
  
  
  

  
  you are right, probably it is a simplification for well known integral representations of pi
  – zeraoulia rafik
  Jul 21 at 2:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  indded see the link in the answer
  – user577488
  Jul 21 at 2:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
  – zeraoulia rafik
  Jul 21 at 2:44
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  you are right, probably it is a simplification for well known integral representations of pi
  – zeraoulia rafik
  Jul 21 at 2:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  indded see the link in the answer
  – user577488
  Jul 21 at 2:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
  – zeraoulia rafik
  Jul 21 at 2:44
  
  

  
  
  
  

you are right, probably it is a simplification for well known integral representations of pi
– zeraoulia rafik
Jul 21 at 2:32

you are right, probably it is a simplification for well known integral representations of pi
– zeraoulia rafik
Jul 21 at 2:32

indded see the link in the answer
– user577488
Jul 21 at 2:37

indded see the link in the answer
– user577488
Jul 21 at 2:37

Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
– zeraoulia rafik
Jul 21 at 2:44

Ok, I don't know if that was montioned in 16 formula representation of pi i linked above in question
– zeraoulia rafik
Jul 21 at 2:44

add a comment | 

 

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