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

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

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

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

2 e^{t} + C

Solution steps

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

Apply u-substitution

: \int 2 e^{u} d u

= \int 2 e^{u} d u

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{u}

Substitute back

u = t

= 2 e^{t}

Add a constant to the solution

= 2 e^{t} + C

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\int_{0}^{1} \frac{1}{x ^{5}} d x

5 t \frac{d y}{d t} + y = t^{4}

h \to 0 lim (\frac{ln ( e + h ) - 1}{h})

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