Primitive of x squared over x squared minus a squared

Theorem

Logarithm Form

$\ds \int \frac {x^2 \rd x} {x^2 - a^2} = x + \frac a 2 \map \ln {\frac {x - a} {x + a} } + C$

for $x^2 > a^2$.

Inverse Hyperbolic Cotangent Form

$\ds \int \frac {x^2 \rd x} {x^2 - a^2} = x - a \coth^{-1} \frac x a + C$

for $x^2 > a^2$.

Also see

• Primitive of $\dfrac {x^2} {a^2 - x^2}$