What is the integral of ge^{kt} ?

The integral of ge^{kt} is (e^{kt}g^2)/2+C

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integral of ge^{kt}

\int g e^{k t}

\frac{e ^{k t} g ^{2}}{2} + C

Solution steps

\int g e^{k t} d g

Take the constant out:

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

= e^{k t} \cdot \int g d g

Apply the Power Rule

: \frac{g ^{2}}{2}

= e^{k t} \frac{g ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{k t} g ^{2}}{2}

Add a constant to the solution

= \frac{e ^{k t} g ^{2}}{2} + C

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