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

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

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

integral

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

\frac{1}{2} Ei (x^{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{2 u} d u

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

Use the nonelementary integral:

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

= \frac{1}{2} Ei (u)

Substitute back

u = x^{2}

= \frac{1}{2} Ei (x^{2})

Add a constant to the solution

= \frac{1}{2} Ei (x^{2}) + C

\frac{x ^{2} - 12 x + 13}{x}

\frac{( x + 3 )}{( x - 1 )}

\frac{1}{( e ^{x^{2}} )}

\frac{( 2 x + 1 )}{( 3 x + 2 )}

(t - x)^{3} sin (x)

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