|
|
|
|
|
|
|
|
|
|
|
|
Integral de $$$x^{4} - x^{3}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \left(x^{4} - x^{3}\right)\, dx$$$.
Solución
Integra término a término:
$${\color{red}{\int{\left(x^{4} - x^{3}\right)d x}}} = {\color{red}{\left(- \int{x^{3} d x} + \int{x^{4} d x}\right)}}$$
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=4$$$:
$$- \int{x^{3} d x} + {\color{red}{\int{x^{4} d x}}}=- \int{x^{3} d x} + {\color{red}{\frac{x^{1 + 4}}{1 + 4}}}=- \int{x^{3} d x} + {\color{red}{\left(\frac{x^{5}}{5}\right)}}$$
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=3$$$:
$$\frac{x^{5}}{5} - {\color{red}{\int{x^{3} d x}}}=\frac{x^{5}}{5} - {\color{red}{\frac{x^{1 + 3}}{1 + 3}}}=\frac{x^{5}}{5} - {\color{red}{\left(\frac{x^{4}}{4}\right)}}$$
Por lo tanto,
$$\int{\left(x^{4} - x^{3}\right)d x} = \frac{x^{5}}{5} - \frac{x^{4}}{4}$$
Simplificar:
$$\int{\left(x^{4} - x^{3}\right)d x} = \frac{x^{4} \left(4 x - 5\right)}{20}$$
Añade la constante de integración:
$$\int{\left(x^{4} - x^{3}\right)d x} = \frac{x^{4} \left(4 x - 5\right)}{20}+C$$
Respuesta
$$$\int \left(x^{4} - x^{3}\right)\, dx = \frac{x^{4} \left(4 x - 5\right)}{20} + C$$$A