# Category:Primitive of Reciprocal of x squared minus a squared

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This category contains pages concerning **Primitive of $\dfrac 1 {x^2 - a^2}$**:

Let $a \in \R_{>0}$ be a strictly positive real constant.

### Inverse Hyperbolic Function Form

- $\ds \int \dfrac {\d x} {x^2 - a^2} = \begin {cases} -\dfrac 1 a \tanh^{-1} \dfrac x a + C & : \size x < a \\ & \\ -\dfrac 1 a \coth^{-1} \dfrac x a + C & : \size x > a \\ & \\ \text {undefined} & : x = a \end {cases}$

### $1$st Logarithm Form

- $\ds \int \frac {\d x} {x^2 - a^2} = \begin {cases} \dfrac 1 {2 a} \map \ln {\dfrac {a - x} {a + x} } + C & : \size x < a\\ & \\ \dfrac 1 {2 a} \map \ln {\dfrac {x - a} {x + a} } + C & : \size x > a \\ & \\ \text {undefined} & : \size x = a \end {cases}$

### $2$nd Logarithm Form

- $\ds \int \frac {\d x} {x^2 - a^2} = \frac 1 {2 a} \ln \size {\frac {x - a} {x + a} } + C$

## Pages in category "Primitive of Reciprocal of x squared minus a squared"

The following 14 pages are in this category, out of 14 total.

### P

- Primitive of Reciprocal of x squared minus a squared
- Primitive of Reciprocal of x squared minus a squared/Inverse Hyperbolic Cotangent Form
- Primitive of Reciprocal of x squared minus a squared/Inverse Hyperbolic Cotangent Form/Proof
- Primitive of Reciprocal of x squared minus a squared/Inverse Hyperbolic Function Form
- Primitive of Reciprocal of x squared minus a squared/Inverse Hyperbolic Tangent Form
- Primitive of Reciprocal of x squared minus a squared/Inverse Hyperbolic Tangent Form/Proof
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 1/size of x greater than a
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 1/size of x less than a
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 2
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 2/Proof 1
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 2/Proof 2
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form 2/Proof 3
- Primitive of Reciprocal of x squared minus a squared/Logarithm Form/Lemma