What is the integral of 5e^{t/(100)} ?

The integral of 5e^{t/(100)} is 500e^{t/(100)}+C

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integral of 5e^{t/(100)}

\int 5 e^{\frac{t}{100}} d t

500 e^{\frac{t}{100}} + C

Solution steps

\int 5 e^{\frac{t}{100}} d t

Take the constant out:

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

= 5 \cdot \int e^{\frac{t}{100}} d t

Apply u-substitution

: \int e^{u} \cdot 100 d u

= 5 \cdot \int e^{u} \cdot 100 d u

Take the constant out:

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

= 5 \cdot 100 \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot 100 e^{u}

Substitute back

u = \frac{t}{100}

= 5 \cdot 100 e^{\frac{t}{100}}

Simplify

= 500 e^{\frac{t}{100}}

Add a constant to the solution

= 500 e^{\frac{t}{100}} + C

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What is the integral of 5e^{t/(100)} ?
The integral of 5e^{t/(100)} is 500e^{t/(100)}+C