$$$11^{- k} 4^{k}$$$의 적분

$$$\int 11^{- k} 4^{k}\, dk$$$을(를) 구하시오.

입력이 다음과 같이 다시 쓰입니다: $$$\int{11^{- k} 4^{k} d k}=\int{\left(\frac{4}{11}\right)^{k} d k}$$$.

Apply the exponential rule $$$\int{a^{k} d k} = \frac{a^{k}}{\ln{\left(a \right)}}$$$ with $$$a=\frac{4}{11}$$$:

$${\color{red}{\int{\left(\frac{4}{11}\right)^{k} d k}}} = {\color{red}{\frac{\left(\frac{4}{11}\right)^{k}}{\ln{\left(\frac{4}{11} \right)}}}}$$

따라서,

$$\int{\left(\frac{4}{11}\right)^{k} d k} = \frac{\left(\frac{4}{11}\right)^{k}}{\ln{\left(\frac{4}{11} \right)}}$$

간단히 하시오:

$$\int{\left(\frac{4}{11}\right)^{k} d k} = \frac{\left(\frac{4}{11}\right)^{k}}{- \ln{\left(11 \right)} + 2 \ln{\left(2 \right)}}$$

적분 상수를 추가하세요:

$$\int{\left(\frac{4}{11}\right)^{k} d k} = \frac{\left(\frac{4}{11}\right)^{k}}{- \ln{\left(11 \right)} + 2 \ln{\left(2 \right)}}+C$$

$$$\int 11^{- k} 4^{k}\, dk = \frac{\left(\frac{4}{11}\right)^{k}}{- \ln\left(11\right) + 2 \ln\left(2\right)} + C$$$A