Rules of Integration (Leaving Cert Applied Maths): Flashcards

Reverses differentiation

$\int x^n dx = \frac{x^{n+1}}{n+1} + c$

Add 1 to power, divide by new power

Derivative of any constant is zero

Integrating with respect to variable $x$

$\ln|x| + c$

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

$\frac{1}{a}e^{ax} + c$

$-\frac{1}{a}\cos(ax) + c$

$\frac{1}{a}\sin(ax) + c$

$\sin^{-1}(\frac{x}{a}) + c$

$\frac{1}{a}\tan^{-1}(\frac{x}{a}) + c$

No, give specific numerical value

$F(b) - F(a)$ where $F$ is antiderivative