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