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

The integral of e^{x^2-x} is \sqrt[4]{e}(sqrt(pi))/2 \erfi(x-1/2)+C

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integral of e^{x^2-x}

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

Solution steps

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

Complete the square

x^{2} - x : (x - \frac{1}{2})^{2} - \frac{1}{4}

= \int e^{(x - \frac{1}{2})^{2} - \frac{1}{4}} d x

Apply u-substitution

: \int e^{u^{2} - \frac{1}{4}} d u

= \int e^{u^{2} - \frac{1}{4}} d u

Simplify

Take the constant out:

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

Use the nonelementary integral:

\int e^{u^{2}} d u = \frac{π}{2} erfi (u)

Substitute back

u = x - \frac{1}{2}

Add a constant to the solution

\frac{\partial}{\partial x} (arccos (\frac{x}{x ^{2} + y ^{2}}))

\frac{d}{d x} (5 x + \frac{400}{x})

7 y^{^{'}} = y^{2}

f (x) = x e^{3 x^{2} + 1}

\int \frac{1}{( y + 1 ) ( y - 2 )} d y

What is the integral of e^{x^2-x} ?
The integral of e^{x^2-x} is \sqrt[4]{e}(sqrt(pi))/2 \erfi(x-1/2)+C