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Integral de $$$\frac{1}{n^{\frac{3}{2}}}$$$
Calculadora relacionada: Calculadora de Integrais Definidas e Impróprias
Sua entrada
Encontre $$$\int \frac{1}{n^{\frac{3}{2}}}\, dn$$$.
Solução
Aplique a regra da potência $$$\int n^{n}\, dn = \frac{n^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=- \frac{3}{2}$$$:
$${\color{red}{\int{\frac{1}{n^{\frac{3}{2}}} d n}}}={\color{red}{\int{n^{- \frac{3}{2}} d n}}}={\color{red}{\frac{n^{- \frac{3}{2} + 1}}{- \frac{3}{2} + 1}}}={\color{red}{\left(- 2 n^{- \frac{1}{2}}\right)}}={\color{red}{\left(- \frac{2}{\sqrt{n}}\right)}}$$
Portanto,
$$\int{\frac{1}{n^{\frac{3}{2}}} d n} = - \frac{2}{\sqrt{n}}$$
Adicione a constante de integração:
$$\int{\frac{1}{n^{\frac{3}{2}}} d n} = - \frac{2}{\sqrt{n}}+C$$
Resposta
$$$\int \frac{1}{n^{\frac{3}{2}}}\, dn = - \frac{2}{\sqrt{n}} + C$$$A