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

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

x \to 3 lim (\frac{5}{2 x - 6})

\int (5 - 3 x) e^{2 x + 3} d x

\int \frac{1}{x ( x + 1 ) ^{3}} d x

\frac{\partial}{\partial x} (4 x + 4 y)

\frac{\partial ^{2}}{\partial u ( w ) \partial w} (e^{u (w) - w})

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