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Integral dari $$$\frac{1}{\sqrt{u}}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{1}{\sqrt{u}}\, du$$$.
Solusi
Terapkan aturan pangkat $$$\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=- \frac{1}{2}$$$:
$${\color{red}{\int{\frac{1}{\sqrt{u}} d u}}}={\color{red}{\int{u^{- \frac{1}{2}} d u}}}={\color{red}{\frac{u^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}}}={\color{red}{\left(2 u^{\frac{1}{2}}\right)}}={\color{red}{\left(2 \sqrt{u}\right)}}$$
Oleh karena itu,
$$\int{\frac{1}{\sqrt{u}} d u} = 2 \sqrt{u}$$
Tambahkan konstanta integrasi:
$$\int{\frac{1}{\sqrt{u}} d u} = 2 \sqrt{u}+C$$
Jawaban
$$$\int \frac{1}{\sqrt{u}}\, du = 2 \sqrt{u} + C$$$A