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

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

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integral of 4e^{-x^2}

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

2 π erf (x) + C

Solution steps

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= 4 \cdot \frac{π}{2} erf (x)

Simplify

4 \cdot \frac{π}{2} erf (x) : 2 π erf (x)

= 2 π erf (x)

Add a constant to the solution

= 2 π erf (x) + C

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