What is the integral of (e^{8sqrt(t)})/(sqrt(t)) ?

The integral of (e^{8sqrt(t)})/(sqrt(t)) is 1/4 e^{8sqrt(t)}+C

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integral of (e^{8sqrt(t)})/(sqrt(t))

\int \frac{e ^{8 t}}{t} d t

\frac{1}{4} e^{8 t} + C

Solution steps

\int \frac{e ^{8 t}}{t} d t

Apply u-substitution

= \int \frac{e ^{u}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 8 t

= \frac{1}{4} e^{8 t}

Add a constant to the solution

= \frac{1}{4} e^{8 t} + C

What is the integral of (e^{8sqrt(t)})/(sqrt(t)) ?
The integral of (e^{8sqrt(t)})/(sqrt(t)) is 1/4 e^{8sqrt(t)}+C