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Integral dari $$$\frac{3}{t}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \frac{3}{t}\, dt$$$.
Solusi
Terapkan aturan pengali konstanta $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ dengan $$$c=3$$$ dan $$$f{\left(t \right)} = \frac{1}{t}$$$:
$${\color{red}{\int{\frac{3}{t} d t}}} = {\color{red}{\left(3 \int{\frac{1}{t} d t}\right)}}$$
Integral dari $$$\frac{1}{t}$$$ adalah $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:
$$3 {\color{red}{\int{\frac{1}{t} d t}}} = 3 {\color{red}{\ln{\left(\left|{t}\right| \right)}}}$$
Oleh karena itu,
$$\int{\frac{3}{t} d t} = 3 \ln{\left(\left|{t}\right| \right)}$$
Tambahkan konstanta integrasi:
$$\int{\frac{3}{t} d t} = 3 \ln{\left(\left|{t}\right| \right)}+C$$
Jawaban
$$$\int \frac{3}{t}\, dt = 3 \ln\left(\left|{t}\right|\right) + C$$$A