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$$$3^{t}$$$の積分
入力内容
$$$\int 3^{t}\, dt$$$ を求めよ。
解答
Apply the exponential rule $$$\int{a^{t} d t} = \frac{a^{t}}{\ln{\left(a \right)}}$$$ with $$$a=3$$$:
$${\color{red}{\int{3^{t} d t}}} = {\color{red}{\frac{3^{t}}{\ln{\left(3 \right)}}}}$$
したがって、
$$\int{3^{t} d t} = \frac{3^{t}}{\ln{\left(3 \right)}}$$
積分定数を加える:
$$\int{3^{t} d t} = \frac{3^{t}}{\ln{\left(3 \right)}}+C$$
解答
$$$\int 3^{t}\, dt = \frac{3^{t}}{\ln\left(3\right)} + C$$$A
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