Primitive of x squared over a squared minus x squared

Theorem

Logarithm Form

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

for $x^2 < a^2$.

Inverse Hyperbolic Tangent Form

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

for $x^2 < a^2$.

Also see

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