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

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

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integral from x to x^3 of e^{t^2}

\int_{x}^{x^{3}} e^{t^{2}} d t

\frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

Solution steps

\int_{x}^{x^{3}} e^{t^{2}} d t

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (t)]_{x}^{x^{3}}

Compute the boundaries:

\frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

= \frac{π}{2} erfi (x^{3}) - \frac{π}{2} erfi (x)

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