$$$a$$$에 대한 $$$\frac{2^{a}}{b}$$$의 적분

$$$\int \frac{2^{a}}{b}\, da$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$을 $$$c=\frac{1}{b}$$$와 $$$f{\left(a \right)} = 2^{a}$$$에 적용하세요:

$${\color{red}{\int{\frac{2^{a}}{b} d a}}} = {\color{red}{\frac{\int{2^{a} d a}}{b}}}$$

Apply the exponential rule $$$\int{a^{a} d a} = \frac{a^{a}}{\ln{\left(a \right)}}$$$ with $$$a=2$$$:

$$\frac{{\color{red}{\int{2^{a} d a}}}}{b} = \frac{{\color{red}{\frac{2^{a}}{\ln{\left(2 \right)}}}}}{b}$$

따라서,

$$\int{\frac{2^{a}}{b} d a} = \frac{2^{a}}{b \ln{\left(2 \right)}}$$

적분 상수를 추가하세요:

$$\int{\frac{2^{a}}{b} d a} = \frac{2^{a}}{b \ln{\left(2 \right)}}+C$$

$$$\int \frac{2^{a}}{b}\, da = \frac{2^{a}}{b \ln\left(2\right)} + C$$$A