Primitive of Reciprocal of a x squared plus b x plus c/Also presented as

Primitive of $\dfrac 1 {a x^2 + b x + c}$: Also presented as

In some older works, this result can also be seen presented as:

$\ds \int \frac {\d x} {a x^2 + 2 b x + c}$

where the solution is then developed via the form:

$\ds \dfrac 1 a \int \frac {\d x} {\paren {x + \frac b a}^2 + \paren {\frac c a - \frac {b^2} {a^2} } }$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Integration: Algebraic Integration