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Integral of $$$3^{t}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int 3^{t}\, dt$$$.
Solution
Apply the exponential rule $$$\int{a^{t} d t} = \frac{a^{t}}{\ln{\left(a \right)}}$$$ with $$$a=3$$$:
$${\color{red}{\int{3^{t} d t}}} = {\color{red}{\frac{3^{t}}{\ln{\left(3 \right)}}}}$$
Therefore,
$$\int{3^{t} d t} = \frac{3^{t}}{\ln{\left(3 \right)}}$$
Add the constant of integration:
$$\int{3^{t} d t} = \frac{3^{t}}{\ln{\left(3 \right)}}+C$$
Answer
$$$\int 3^{t}\, dt = \frac{3^{t}}{\ln\left(3\right)} + C$$$A
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