|
|
|
|
|
|
|
|
|
|
|
|
Integral de $$$\frac{1}{\sqrt{u^{2} + 1}}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{\sqrt{u^{2} + 1}}\, du$$$.
Solución
La integral de $$$\frac{1}{\sqrt{u^{2} + 1}}$$$ es $$$\int{\frac{1}{\sqrt{u^{2} + 1}} d u} = \operatorname{asinh}{\left(u \right)}$$$:
$${\color{red}{\int{\frac{1}{\sqrt{u^{2} + 1}} d u}}} = {\color{red}{\operatorname{asinh}{\left(u \right)}}}$$
Por lo tanto,
$$\int{\frac{1}{\sqrt{u^{2} + 1}} d u} = \operatorname{asinh}{\left(u \right)}$$
Añade la constante de integración:
$$\int{\frac{1}{\sqrt{u^{2} + 1}} d u} = \operatorname{asinh}{\left(u \right)}+C$$
Respuesta
$$$\int \frac{1}{\sqrt{u^{2} + 1}}\, du = \operatorname{asinh}{\left(u \right)} + C$$$A