What is the integral of 1/x e^{x^2} ?

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

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integral of 1/x e^{x^2}

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

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

Solution steps

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

Simplify

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

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

Apply u-substitution

= \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

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