Integraal van $$$- \frac{i a l m \mu^{a l m} n t}{2}$$$ met betrekking tot $$$t$$$

Bepaal $$$\int \left(- \frac{i a l m \mu^{a l m} n t}{2}\right)\, dt$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ toe met $$$c=- \frac{i a l m \mu^{a l m} n}{2}$$$ en $$$f{\left(t \right)} = t$$$:

$${\color{red}{\int{\left(- \frac{i a l m \mu^{a l m} n t}{2}\right)d t}}} = {\color{red}{\left(- \frac{i a l m \mu^{a l m} n \int{t d t}}{2}\right)}}$$

Pas de machtsregel $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=1$$$:

$$- \frac{i a l m \mu^{a l m} n {\color{red}{\int{t d t}}}}{2}=- \frac{i a l m \mu^{a l m} n {\color{red}{\frac{t^{1 + 1}}{1 + 1}}}}{2}=- \frac{i a l m \mu^{a l m} n {\color{red}{\left(\frac{t^{2}}{2}\right)}}}{2}$$

Dus,

$$\int{\left(- \frac{i a l m \mu^{a l m} n t}{2}\right)d t} = - \frac{i a l m \mu^{a l m} n t^{2}}{4}$$

Voeg de integratieconstante toe:

$$\int{\left(- \frac{i a l m \mu^{a l m} n t}{2}\right)d t} = - \frac{i a l m \mu^{a l m} n t^{2}}{4}+C$$

$$$\int \left(- \frac{i a l m \mu^{a l m} n t}{2}\right)\, dt = - \frac{i a l m \mu^{a l m} n t^{2}}{4} + C$$$A