What is the integral from 2x to x+5 of e^{t^2+1} ?

The integral from 2x to x+5 of e^{t^2+1} is e((sqrt(pi))/2 \erfi(x+5)-(sqrt(pi))/2 \erfi(2x))

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integral from 2x to x+5 of e^{t^2+1}

\int_{2 x}^{x + 5} e^{t^{2} + 1} d t

e (\frac{π}{2} erfi (x + 5) - \frac{π}{2} erfi (2 x))

Solution steps

\int_{2 x}^{x + 5} e^{t^{2} + 1} d t

e^{t^{2} + 1} = e^{1} e^{t^{2}}

= \int_{2 x}^{x + 5} e^{1} e^{t^{2}} d t

Take the constant out:

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

= e^{1} \cdot \int_{2 x}^{x + 5} e^{t^{2}} d t

Simplify

= e \cdot \int_{2 x}^{x + 5} e^{t^{2}} d t

Use the nonelementary integral:

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

= e [\frac{π}{2} erfi (t)]_{2 x}^{x + 5}

Compute the boundaries:

\frac{π}{2} erfi (x + 5) - \frac{π}{2} erfi (2 x)

= e (\frac{π}{2} erfi (x + 5) - \frac{π}{2} erfi (2 x))

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What is the integral from 2x to x+5 of e^{t^2+1} ?
The integral from 2x to x+5 of e^{t^2+1} is e((sqrt(pi))/2 \erfi(x+5)-(sqrt(pi))/2 \erfi(2x))