What is the integral of e/(e^{(x)^2)} ?

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

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integral of e/(e^{(x)^2)}

integral

\frac{e}{e ^{(x)^{2}}}

e \frac{π}{2} erf (x) + C

Solution steps

\int \frac{e}{e ^{x^{2}}} d x

Take the constant out:

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

= e \cdot \int \frac{1}{e ^{x^{2}}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{x^{2}}} = e^{- x^{2}}

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

Use the nonelementary integral:

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

= e \frac{π}{2} erf (x)

Add a constant to the solution

= e \frac{π}{2} erf (x) + C

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