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Integral dari $$$\frac{1}{x^{6}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{1}{x^{6}}\, dx$$$.
Solusi
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-6$$$:
$${\color{red}{\int{\frac{1}{x^{6}} d x}}}={\color{red}{\int{x^{-6} d x}}}={\color{red}{\frac{x^{-6 + 1}}{-6 + 1}}}={\color{red}{\left(- \frac{x^{-5}}{5}\right)}}={\color{red}{\left(- \frac{1}{5 x^{5}}\right)}}$$
Oleh karena itu,
$$\int{\frac{1}{x^{6}} d x} = - \frac{1}{5 x^{5}}$$
Tambahkan konstanta integrasi:
$$\int{\frac{1}{x^{6}} d x} = - \frac{1}{5 x^{5}}+C$$
Jawaban
$$$\int \frac{1}{x^{6}}\, dx = - \frac{1}{5 x^{5}} + C$$$A