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