What is the integral from 0 to 1 of 13e^{x^2} ?

The integral from 0 to 1 of 13e^{x^2} is (13sqrt(pi))/2 \erfi(1)

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integral from 0 to 1 of 13e^{x^2}

\int_{0}^{1} 13 e^{x^{2}} d x

\frac{13 π}{2} erfi (1)

Solution steps

\int_{0}^{1} 13 e^{x^{2}} d x

Take the constant out:

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

= 13 \cdot \int_{0}^{1} e^{x^{2}} d x

Use the nonelementary integral:

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

= 13 [\frac{π}{2} erfi (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} erfi (1)

= 13 \cdot \frac{π}{2} erfi (1)

Simplify

= \frac{13 π}{2} erfi (1)

x \to 4 lim (- x + 4)

\int (4 e^{x} + 12 x^{\frac{3}{2}} + 4 x^{\frac{1}{2}}) d x

x^{2} - 4, at x = 3

\frac{ln ( x )}{10 x}

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

What is the integral from 0 to 1 of 13e^{x^2} ?
The integral from 0 to 1 of 13e^{x^2} is (13sqrt(pi))/2 \erfi(1)