Integral dari $$$\frac{1}{x^{2} + 1}$$$

Temukan $$$\int \frac{1}{x^{2} + 1}\, dx$$$.

Integral dari $$$\frac{1}{x^{2} + 1}$$$ adalah $$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$$:

$${\color{red}{\int{\frac{1}{x^{2} + 1} d x}}} = {\color{red}{\operatorname{atan}{\left(x \right)}}}$$

Oleh karena itu,

$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$

Tambahkan konstanta integrasi:

$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}+C$$

$$$\int \frac{1}{x^{2} + 1}\, dx = \operatorname{atan}{\left(x \right)} + C$$$A