What is the integral of 30e^{0.3t} ?

The integral of 30e^{0.3t} is 99.99999…e^{0.3t}+C

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integral of 30e^{0.3t}

\int 30 e^{0.3 t} d t

99.99999 \dots e^{0.3 t} + C

Solution steps

\int 30 e^{0.3 t} d t

Take the constant out:

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

= 30 \cdot \int e^{0.3 t} d t

Apply u-substitution

= 30 \cdot \int e^{u} \frac{1}{0.3} d u

Take the constant out:

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

= 30 \cdot \frac{1}{0.3} \cdot \int e^{u} d u

Simplify

= 30 \cdot 3.33333 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 30 \cdot 3.33333 \dots e^{u}

Substitute back

u = 0.3 t

= 30 \cdot 3.33333 \dots e^{0.3 t}

Simplify

= 99.99999 \dots e^{0.3 t}

Add a constant to the solution

= 99.99999 \dots e^{0.3 t} + C

What is the integral of 30e^{0.3t} ?
The integral of 30e^{0.3t} is 99.99999…e^{0.3t}+C