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Integral dari $$$\frac{1}{r^{3}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{1}{r^{3}}\, dr$$$.
Solusi
Terapkan aturan pangkat $$$\int r^{n}\, dr = \frac{r^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-3$$$:
$${\color{red}{\int{\frac{1}{r^{3}} d r}}}={\color{red}{\int{r^{-3} d r}}}={\color{red}{\frac{r^{-3 + 1}}{-3 + 1}}}={\color{red}{\left(- \frac{r^{-2}}{2}\right)}}={\color{red}{\left(- \frac{1}{2 r^{2}}\right)}}$$
Oleh karena itu,
$$\int{\frac{1}{r^{3}} d r} = - \frac{1}{2 r^{2}}$$
Tambahkan konstanta integrasi:
$$\int{\frac{1}{r^{3}} d r} = - \frac{1}{2 r^{2}}+C$$
Jawaban
$$$\int \frac{1}{r^{3}}\, dr = - \frac{1}{2 r^{2}} + C$$$A