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

The integral of e^{t/5} is 5e^{t/5}+C

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integral of e^{t/5}

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

5 e^{\frac{t}{5}} + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 5 e^{u}

Substitute back

u = \frac{t}{5}

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

Add a constant to the solution

= 5 e^{\frac{t}{5}} + C