What is the integral of 1/(sqrt(x))*e^{sqrt(x)} ?

The integral of 1/(sqrt(x))*e^{sqrt(x)} is 2e^{sqrt(x)}+C

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integral of 1/(sqrt(x))*e^{sqrt(x)}

\int \frac{1}{x} \cdot e^{x} d x

2 e^{x} + C

Solution steps

\int \frac{1}{x} e^{x} d x

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 = x

= 2 e^{x}

Add a constant to the solution

= 2 e^{x} + C

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What is the integral of 1/(sqrt(x))*e^{sqrt(x)} ?
The integral of 1/(sqrt(x))*e^{sqrt(x)} is 2e^{sqrt(x)}+C