# Antiderivative of 1/(x^2 - 1)

1. Mar 1, 2005

### KataKoniK

Do you guys have any tips on how to get the antiderivative of

1 / (x^2 - 1)?

Thanks.

2. Mar 1, 2005

### dextercioby

Yes,simple fractions would be the most direct and elegant way.

Daniel.

3. Mar 1, 2005

### Jameson

$$\int \frac{1}{(x-1)(x+1)}dx = \int {\frac{1}{2(x-1)}} - {\frac{1}{2(x+1)}}dx$$

Last edited: Mar 2, 2005
4. Mar 1, 2005

### dextercioby

That was my first guess.If you wanna do something fancy,how about computing the antiderivative of argument tangent hyperbolicus...?

Daniel.

5. Mar 1, 2005

### Hurkyl

Staff Emeritus
You forgot the dx's. :tongue2:

6. Mar 1, 2005

### KataKoniK

Thanks.

Ans is therefore,

(1/2) ln(x-1) - (1/2) ln(x+1)

7. Mar 1, 2005

### dextercioby

Plus a constant.And you can write it as a natural logarithm of a fraction to which you incorporate the constant.

Daniel.

8. Mar 1, 2005

### KataKoniK

Got it. Thanks.

9. Jan 18, 2012

### clecle4

and if it is bounded at -3 and -2

10. Jan 18, 2012

### DivisionByZro

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.