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Integral dari $$$\sqrt[6]{x}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \sqrt[6]{x}\, dx$$$.
Solusi
Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=\frac{1}{6}$$$:
$${\color{red}{\int{\sqrt[6]{x} d x}}}={\color{red}{\int{x^{\frac{1}{6}} d x}}}={\color{red}{\frac{x^{\frac{1}{6} + 1}}{\frac{1}{6} + 1}}}={\color{red}{\left(\frac{6 x^{\frac{7}{6}}}{7}\right)}}$$
Oleh karena itu,
$$\int{\sqrt[6]{x} d x} = \frac{6 x^{\frac{7}{6}}}{7}$$
Tambahkan konstanta integrasi:
$$\int{\sqrt[6]{x} d x} = \frac{6 x^{\frac{7}{6}}}{7}+C$$
Jawaban
$$$\int \sqrt[6]{x}\, dx = \frac{6 x^{\frac{7}{6}}}{7} + C$$$A