What is the integral from 0 to 1 of e^{3x^2} ?

The integral from 0 to 1 of e^{3x^2} is (sqrt(pi))/(2sqrt(3))\erfi(sqrt(3))

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integral from 0 to 1 of e^{3x^2}

\int_{0}^{1} e^{3 x^{2}} d x

\frac{π}{2 3} erfi (3)

Solution steps

\int_{0}^{1} e^{3 x^{2}} d x

= \int_{0}^{1} e^{(3 x)^{2}} d x

Apply u-substitution

: \int_{0}^{3} e^{u^{2}} \frac{1}{3} d u

= \int_{0}^{3} e^{u^{2}} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{3} e^{u^{2}} d u

Use the nonelementary integral:

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

= \frac{1}{3} [\frac{π}{2} erfi (u)]_{0}^{3}

Compute the boundaries:

\frac{π}{2} erfi (3)

= \frac{1}{3} \cdot \frac{π}{2} erfi (3)

Simplify

= \frac{π}{2 3} erfi (3)

\int_{0}^{2} r^{2} d r

\int_{0}^{3} \frac{3 x}{1 + x} d x

\int_{0}^{x + y} e^{x} (y + 2 z) d z

\int_{0}^{3} \frac{x - 1}{x + 1} d x

\int_{0}^{1} x (x + y) d x

What is the integral from 0 to 1 of e^{3x^2} ?
The integral from 0 to 1 of e^{3x^2} is (sqrt(pi))/(2sqrt(3))\erfi(sqrt(3))