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Integral de $$$\theta \tan{\left(2 \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \theta \tan{\left(2 \right)}\, d\theta$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ con $$$c=\tan{\left(2 \right)}$$$ y $$$f{\left(\theta \right)} = \theta$$$:
$${\color{red}{\int{\theta \tan{\left(2 \right)} d \theta}}} = {\color{red}{\tan{\left(2 \right)} \int{\theta d \theta}}}$$
Aplica la regla de la potencia $$$\int \theta^{n}\, d\theta = \frac{\theta^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=1$$$:
$$\tan{\left(2 \right)} {\color{red}{\int{\theta d \theta}}}=\tan{\left(2 \right)} {\color{red}{\frac{\theta^{1 + 1}}{1 + 1}}}=\tan{\left(2 \right)} {\color{red}{\left(\frac{\theta^{2}}{2}\right)}}$$
Por lo tanto,
$$\int{\theta \tan{\left(2 \right)} d \theta} = \frac{\theta^{2} \tan{\left(2 \right)}}{2}$$
Añade la constante de integración:
$$\int{\theta \tan{\left(2 \right)} d \theta} = \frac{\theta^{2} \tan{\left(2 \right)}}{2}+C$$
Respuesta
$$$\int \theta \tan{\left(2 \right)}\, d\theta = \frac{\theta^{2} \tan{\left(2 \right)}}{2} + C$$$A