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