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