Integral de $$$\frac{i n t^{2} u}{2} + \cos{\left(x \right)}$$$ con respecto a $$$x$$$

Halla $$$\int \left(\frac{i n t^{2} u}{2} + \cos{\left(x \right)}\right)\, dx$$$.

Integra término a término:

$${\color{red}{\int{\left(\frac{i n t^{2} u}{2} + \cos{\left(x \right)}\right)d x}}} = {\color{red}{\left(\int{\frac{i n t^{2} u}{2} d x} + \int{\cos{\left(x \right)} d x}\right)}}$$

Aplica la regla de la constante $$$\int c\, dx = c x$$$ con $$$c=\frac{i n t^{2} u}{2}$$$:

$$\int{\cos{\left(x \right)} d x} + {\color{red}{\int{\frac{i n t^{2} u}{2} d x}}} = \int{\cos{\left(x \right)} d x} + {\color{red}{\left(\frac{i n t^{2} u x}{2}\right)}}$$

La integral del coseno es $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

$$\frac{i n t^{2} u x}{2} + {\color{red}{\int{\cos{\left(x \right)} d x}}} = \frac{i n t^{2} u x}{2} + {\color{red}{\sin{\left(x \right)}}}$$

Por lo tanto,

$$\int{\left(\frac{i n t^{2} u}{2} + \cos{\left(x \right)}\right)d x} = \frac{i n t^{2} u x}{2} + \sin{\left(x \right)}$$

Añade la constante de integración:

$$\int{\left(\frac{i n t^{2} u}{2} + \cos{\left(x \right)}\right)d x} = \frac{i n t^{2} u x}{2} + \sin{\left(x \right)}+C$$

$$$\int \left(\frac{i n t^{2} u}{2} + \cos{\left(x \right)}\right)\, dx = \left(\frac{i n t^{2} u x}{2} + \sin{\left(x \right)}\right) + C$$$A