What is the integral from 0 to 4 of sqrt(x)e^x ?

The integral from 0 to 4 of sqrt(x)e^x is 2e^4-(sqrt(pi))/2 \erfi(sqrt(4))

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integral from 0 to 4 of sqrt(x)e^x

\int_{0}^{4} x e^{x} d x

2 e^{4} - \frac{π}{2} erfi (4)

Solution steps

\int_{0}^{4} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int \frac{e ^{x}}{2 x} d x]_{0}^{4}

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

= [e^{x} x - \frac{π}{2} erfi (x)]_{0}^{4}

Compute the boundaries:

2 e^{4} - \frac{π}{2} erfi (4)

= 2 e^{4} - \frac{π}{2} erfi (4)

What is the integral from 0 to 4 of sqrt(x)e^x ?
The integral from 0 to 4 of sqrt(x)e^x is 2e^4-(sqrt(pi))/2 \erfi(sqrt(4))