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Integral dari $$$\frac{1}{x^{8}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{1}{x^{8}}\, dx$$$.
Solusi
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=-8$$$:
$${\color{red}{\int{\frac{1}{x^{8}} d x}}}={\color{red}{\int{x^{-8} d x}}}={\color{red}{\frac{x^{-8 + 1}}{-8 + 1}}}={\color{red}{\left(- \frac{x^{-7}}{7}\right)}}={\color{red}{\left(- \frac{1}{7 x^{7}}\right)}}$$
Oleh karena itu,
$$\int{\frac{1}{x^{8}} d x} = - \frac{1}{7 x^{7}}$$
Tambahkan konstanta integrasi:
$$\int{\frac{1}{x^{8}} d x} = - \frac{1}{7 x^{7}}+C$$
Jawaban
$$$\int \frac{1}{x^{8}}\, dx = - \frac{1}{7 x^{7}} + C$$$A