What is the integral of e^{4-x^2} ?

The integral of e^{4-x^2} is e^4(sqrt(pi))/2 \erf(x)+C

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integral of e^{4-x^2}

\int e^{4 - x^{2}} d x

e^{4} \frac{π}{2} erf (x) + C

Solution steps

\int e^{4 - x^{2}} d x

Simplify

e^{4 - x^{2}} : e^{4} e^{- x^{2}}

= \int e^{4} e^{- x^{2}} d x

Take the constant out:

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

= e^{4} \cdot \int e^{- x^{2}} d x

Use the nonelementary integral:

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

= e^{4} \frac{π}{2} erf (x)

Add a constant to the solution

= e^{4} \frac{π}{2} erf (x) + C

\int \frac{sin ( x )}{cos ^{3} ( x ) + cos ( x )} d x

\frac{d ^{3}}{d x ^{3}} (x)

e^{4 x}

\int \frac{cos ( ln ( 4 x ^{2} ) )}{x} d x

6 y^{^{'}} = y^{2}, y (0) = 5

What is the integral of e^{4-x^2} ?
The integral of e^{4-x^2} is e^4(sqrt(pi))/2 \erf(x)+C