Rules of Integration (Leaving Cert Applied Maths): Flashcards

Integration

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

Accounts for lost constant (derivative of any constant is zero)

Definite integrals (give specific numerical answers)

$\ln|x| + c$

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

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

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

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

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

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

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

Differentiate result - should get original function back