What is the integral of (e^{3sqrt(t)})/(sqrt(t)) ?

The integral of (e^{3sqrt(t)})/(sqrt(t)) is 2/3 e^{3sqrt(t)}+C

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integral of (e^{3sqrt(t)})/(sqrt(t))

\int \frac{e ^{3 t}}{t} d t

\frac{2}{3} e^{3 t} + C

Solution steps

\int \frac{e ^{3 t}}{t} d t

Apply u-substitution

= \int \frac{2 e ^{u}}{3} d u

Take the constant out:

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

= \frac{2}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{3} e^{u}

Substitute back

u = 3 t

= \frac{2}{3} e^{3 t}

Add a constant to the solution

= \frac{2}{3} e^{3 t} + C

\int in (x) d x

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) ^{5}}

\frac{d}{d x} (4 x^{5} - 5 x^{4})

t an g e n t x^{3} + y^{3} - 6 x y = 0, (\frac{4}{3}, \frac{8}{3})

t an g e n t f (x) = \frac{x ^{2} - 1}{x ^{2} + 1}, at x = 0

What is the integral of (e^{3sqrt(t)})/(sqrt(t)) ?
The integral of (e^{3sqrt(t)})/(sqrt(t)) is 2/3 e^{3sqrt(t)}+C