$$$\frac{1}{1849 \cos^{2}{\left(x \right)}}$$$'nin integrali

Bulun: $$$\int \frac{1}{1849 \cos^{2}{\left(x \right)}}\, dx$$$.

Sabit katsayı kuralı $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$'i $$$c=\frac{1}{1849}$$$ ve $$$f{\left(x \right)} = \frac{1}{\cos^{2}{\left(x \right)}}$$$ ile uygula:

$${\color{red}{\int{\frac{1}{1849 \cos^{2}{\left(x \right)}} d x}}} = {\color{red}{\left(\frac{\int{\frac{1}{\cos^{2}{\left(x \right)}} d x}}{1849}\right)}}$$

İntegrand'ı sekant cinsinden yeniden yazın.:

$$\frac{{\color{red}{\int{\frac{1}{\cos^{2}{\left(x \right)}} d x}}}}{1849} = \frac{{\color{red}{\int{\sec^{2}{\left(x \right)} d x}}}}{1849}$$

$$$\sec^{2}{\left(x \right)}$$$'nin integrali $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:

$$\frac{{\color{red}{\int{\sec^{2}{\left(x \right)} d x}}}}{1849} = \frac{{\color{red}{\tan{\left(x \right)}}}}{1849}$$

Dolayısıyla,

$$\int{\frac{1}{1849 \cos^{2}{\left(x \right)}} d x} = \frac{\tan{\left(x \right)}}{1849}$$

İntegrasyon sabitini ekleyin:

$$\int{\frac{1}{1849 \cos^{2}{\left(x \right)}} d x} = \frac{\tan{\left(x \right)}}{1849}+C$$

$$$\int \frac{1}{1849 \cos^{2}{\left(x \right)}}\, dx = \frac{\tan{\left(x \right)}}{1849} + C$$$A