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