What is the integral of 102e^{0.06t} ?

The integral of 102e^{0.06t} is 1700.00000…e^{0.06t}+C

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integral of 102e^{0.06t}

\int 102 e^{0.06 t} d t

1700.00000 \dots e^{0.06 t} + C

Solution steps

\int 102 e^{0.06 t} d t

Take the constant out:

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

= 102 \cdot \int e^{0.06 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{0.06} d u

= 102 \cdot \int e^{u} \frac{1}{0.06} d u

Take the constant out:

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

= 102 \cdot \frac{1}{0.06} \cdot \int e^{u} d u

Simplify

= 102 \cdot 16.66666 \dots \cdot \int e^{u} d u

Use the common integral:

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

= 102 \cdot 16.66666 \dots e^{u}

Substitute back

u = 0.06 t

= 102 \cdot 16.66666 \dots e^{0.06 t}

Simplify

= 1700.00000 \dots e^{0.06 t}

Add a constant to the solution

= 1700.00000 \dots e^{0.06 t} + C

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What is the integral of 102e^{0.06t} ?
The integral of 102e^{0.06t} is 1700.00000…e^{0.06t}+C