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

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

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integral of e^{sqrt(x)}*1/(2sqrt(x))

\int e^{x} \cdot \frac{1}{2 x} d x

e^{x} + C

Solution steps

\int e^{x} \frac{1}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{x} \frac{1}{x} d x

Apply u-substitution

: \int 2 e^{u} d u

= \frac{1}{2} \cdot \int 2 e^{u} d u

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{u}

Substitute back

u = x

= \frac{1}{2} \cdot 2 e^{x}

Simplify

\frac{1}{2} \cdot 2 e^{x} : e^{x}

= e^{x}

Add a constant to the solution

= e^{x} + C

\int_{- \infty}^{6} r e^{\frac{r}{3}} d r

\frac{d}{d x} (\frac{x ^{2} + x - 2}{2 x ^{2} - 2})

f (x) = x^{5 x}

\int u^{- 3} (4 - u^{3} + u^{6}) d u

e^{x} (x^{3} - 3 x^{2} + 6 x - 6)

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