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