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

The integral of (e^{x/2})/x is \Ei(x/2)+C

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integral of (e^{x/2})/x

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

Ei (\frac{x}{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{u} d u

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = \frac{x}{2}

= Ei (\frac{x}{2})

Add a constant to the solution

= Ei (\frac{x}{2}) + C

\int 7 x^{3} + 4 x^{2} d x

\frac{3}{2 x}

\frac{d}{d x} (ln ((x - 3)^{2}))

x

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{1}{x ^{8}})