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

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

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

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

2 e^{x} + C

Solution steps

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

\int \frac{1}{x + 2 + x} d x

\int x - x^{2} + 3 x - 2 d x

\frac{d}{d t} (a cos (4 t) + b sin (4 t))

ln (2 cos^{4} (θ))

(x e^{x})^{^{'}}

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