Integral dari $$$\left(\frac{1003}{1000}\right)^{x}$$$
Kalkulator terkait: Kalkulator Integral Tentu dan Tak Wajar
Masukan Anda
Temukan $$$\int \left(\frac{1003}{1000}\right)^{x}\, dx$$$.
Solusi
Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=\frac{1003}{1000}$$$:
$${\color{red}{\int{\left(\frac{1003}{1000}\right)^{x} d x}}} = {\color{red}{\frac{\left(\frac{1003}{1000}\right)^{x}}{\ln{\left(\frac{1003}{1000} \right)}}}}$$
Oleh karena itu,
$$\int{\left(\frac{1003}{1000}\right)^{x} d x} = \frac{\left(\frac{1003}{1000}\right)^{x}}{\ln{\left(\frac{1003}{1000} \right)}}$$
Sederhanakan:
$$\int{\left(\frac{1003}{1000}\right)^{x} d x} = \frac{\left(\frac{1003}{1000}\right)^{x}}{- 3 \ln{\left(10 \right)} + \ln{\left(1003 \right)}}$$
Tambahkan konstanta integrasi:
$$\int{\left(\frac{1003}{1000}\right)^{x} d x} = \frac{\left(\frac{1003}{1000}\right)^{x}}{- 3 \ln{\left(10 \right)} + \ln{\left(1003 \right)}}+C$$
Jawaban
$$$\int \left(\frac{1003}{1000}\right)^{x}\, dx = \frac{\left(\frac{1003}{1000}\right)^{x}}{- 3 \ln\left(10\right) + \ln\left(1003\right)} + C$$$A