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