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

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

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

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

\frac{3 π}{2} erfi (1)

Solution steps

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= 3 [\frac{π}{2} erfi (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} erfi (1)

= 3 \cdot \frac{π}{2} erfi (1)

Simplify

= \frac{3 π}{2} erfi (1)

f (x) = x^{3} + 2 x^{2} + 4 x, at x = - 1

f (x) = (2 x - 3) (x + 3)^{3}

\int \frac{x ^{- 1} - x ^{- 3} + x ^{- 3}}{x ^{2}} d x

\frac{d}{d x} (\frac{( 3 x ^{2} - 5 )}{( 2 x ^{2} + 1 )})

f (x) = e^{x^{4}}

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