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