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

x \to 3 lim (5 x^{2} - 3 x + 5)

\int \frac{( cos ^{2} ( x ) )}{( sin ^{2} ( x ) )} d x

\int \frac{1}{x ^{2} + 4 x + 10} d x

y cos^{2} (x) \frac{d y}{d x} = 4 + tan^{2} (x)

\int x + 7 d x

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