What is the integral of e^{x^2+3} ?

The integral of e^{x^2+3} is e^3(sqrt(pi))/2 \erfi(x)+C

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integral of e^{x^2+3}

\int e^{x^{2} + 3} d x

e^{3} \frac{π}{2} erfi (x) + C

Solution steps

\int e^{x^{2} + 3} d x

Simplify

e^{x^{2} + 3} : e^{x^{2}} e^{3}

= \int e^{x^{2}} e^{3} d x

Take the constant out:

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

= e^{3} \cdot \int e^{x^{2}} d x

Use the nonelementary integral:

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

= e^{3} \frac{π}{2} erfi (x)

Add a constant to the solution

= e^{3} \frac{π}{2} erfi (x) + C

y = 8 x - x^{2}, (1, 7)

y^{^{''}} - 2 y^{^{'}} - 8 y = 0 y (0) = - 2, y^{^{'}} (0) = 4

\int \frac{t + 2 t ^{2}}{t} d t

\frac{x d y}{d x} = 4 y

n = 1 \sum \infty \frac{1}{1 + ln ( n )}

What is the integral of e^{x^2+3} ?
The integral of e^{x^2+3} is e^3(sqrt(pi))/2 \erfi(x)+C