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