What is the integral of 0.5e^t ?

The integral of 0.5e^t is 0.5e^t+C

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integral of 0.5e^t

\int 0.5 e^{t} d t

0.5 e^{t} + C

Solution steps

\int 0.5 e^{t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 0.5 \cdot \int e^{t} d t

Use the common integral:

\int e^{t} d t = e^{t}

= 0.5 e^{t}

Add a constant to the solution

= 0.5 e^{t} + C