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

The integral of sqrt(e^{5t)} is 2/5 e^{(5t)/2}+C

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integral of sqrt(e^{5t)}

\int e^{5 t} d t

\frac{2}{5} e^{\frac{5 t}{2}} + C

Solution steps

\int e^{5 t} d t

Apply radical rule:

assuming

a \geq 0

= \int e^{\frac{5 t}{2}} d t

Apply u-substitution

= \int e^{u} \frac{2}{5} d u

Take the constant out:

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

= \frac{2}{5} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{5} e^{u}

Substitute back

u = \frac{5 t}{2}

= \frac{2}{5} e^{\frac{5 t}{2}}

Add a constant to the solution

= \frac{2}{5} e^{\frac{5 t}{2}} + C

What is the integral of sqrt(e^{5t)} ?
The integral of sqrt(e^{5t)} is 2/5 e^{(5t)/2}+C