- #1
KataKoniK
- 1,347
- 0
Do you guys have any tips on how to get the antiderivative of
1 / (x^2 - 1)?
Thanks.
1 / (x^2 - 1)?
Thanks.
How can I find the antiderivative of 1 / (x^2 - 1)?
- Thread starter KataKoniK
- Start date
-
- Tags
- Antiderivative
In summary, the conversation is about finding the antiderivative of 1/(x^2-1). The suggestion is to use simple fractions for a direct and elegant solution. One person also suggests using the antiderivative of argument tangent hyperbolicus. The correct answer is (1/2) ln(x-1) - (1/2) ln(x+1) plus a constant, which can also be written as a natural logarithm of a fraction with the constant incorporated. There is also a reminder not to revive old threads for homework questions.
- #2
- 13,366
- 3,506
Yes,simple fractions would be the most direct and elegant way.
Daniel.
Daniel.
- #3
Jameson
Gold Member
MHB
- 4,541
- 13
[tex]\int \frac{1}{(x-1)(x+1)}dx = \int {\frac{1}{2(x-1)}} - {\frac{1}{2(x+1)}}dx[/tex]
Last edited by a moderator:
- #4
- 13,366
- 3,506
That was my first guess.If you want to do something fancy,how about computing the antiderivative of argument tangent hyperbolicus...?
Daniel.
Daniel.
- #5
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
- 14,983
- 28
You forgot the dx's. 
- #6
KataKoniK
- 1,347
- 0
Thanks.
Ans is therefore,
(1/2) ln(x-1) - (1/2) ln(x+1)
Ans is therefore,
(1/2) ln(x-1) - (1/2) ln(x+1)
- #7
- 13,366
- 3,506
Plus a constant.And you can write it as a natural logarithm of a fraction to which you incorporate the constant.
Daniel.
Daniel.
- #8
KataKoniK
- 1,347
- 0
Got it. Thanks.
- #9
clecle4
- 1
- 0
and if it is bounded at -3 and -2
- #10
DivisionByZro
- 252
- 1
The thread is seven years old, why revive it? If you have a homework question please make a new thread instead of resurrecting old ones.
FAQ: How can I find the antiderivative of 1 / (x^2 - 1)?
1. What is the antiderivative of 1/(x^2 - 1)?
The antiderivative of 1/(x^2 - 1) is arctanh(x) + C.
2. How do you find the antiderivative of 1/(x^2 - 1)?
To find the antiderivative of 1/(x^2 - 1), use the substitution method by letting u = x^2 - 1. Then, rewrite the integral in terms of u and use the formula for the antiderivative of 1/u.
3. Is the antiderivative of 1/(x^2 - 1) defined for all values of x?
No, the antiderivative of 1/(x^2 - 1) is not defined for x = 1 or x = -1, as the denominator becomes zero in these cases.
4. Can the antiderivative of 1/(x^2 - 1) be simplified further?
Yes, the antiderivative of 1/(x^2 - 1) can be simplified using trigonometric identities to become (1/2)ln|1 + x| - (1/2)ln|1 - x| + C.
5. What is the domain of the antiderivative of 1/(x^2 - 1)?
The domain of the antiderivative of 1/(x^2 - 1) is all real numbers except for x = 1 and x = -1, as these values make the denominator equal to zero.