What is the integral of e^{x^2-5x} ?

The integral of e^{x^2-5x} is e^6\sqrt[4]{e}(sqrt(pi))/2 \erfi(x-5/2)+C

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integral of e^{x^2-5x}

\int e^{x^{2} - 5 x} d x

Solution steps

\int e^{x^{2} - 5 x} d x

Complete the square

x^{2} - 5 x : (x - \frac{5}{2})^{2} - \frac{25}{4}

= \int e^{(x - \frac{5}{2})^{2} - \frac{25}{4}} d x

Apply u-substitution

: \int e^{u^{2} - \frac{25}{4}} d u

= \int e^{u^{2} - \frac{25}{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{5}{2}

Add a constant to the solution

x \to 0 - lim (\frac{1}{e ^{x}})

\int \frac{1}{- x + 1} d x

\frac{d}{d x} (\frac{x ^{2} + 4}{2 x})

y = 4 - 2 x^{2}

u + 1

What is the integral of e^{x^2-5x} ?
The integral of e^{x^2-5x} is e^6\sqrt[4]{e}(sqrt(pi))/2 \erfi(x-5/2)+C