Integration of the Reciprocal Function (HSC SSCE Mathematics Advanced): Flashcards

$\frac{x^0}{0}$, undefined (division by zero)

$\ln x + C$

$\ln|x| + C$, where $x \neq 0$

$1$

$\frac{1}{a}\ln|ax+b| + C$

$\ln|f(x)| + C$

Numerator must be derivative of denominator

Never cross an asymptote/discontinuity

$x \ln x - x + C$

$0$