What is the integral of sqrt(x)e^x ?

The integral of sqrt(x)e^x is e^xsqrt(x)-(sqrt(pi))/2 \erfi(sqrt(x))+C

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integral of sqrt(x)e^x

\int x e^{x} d x

e^{x} x - \frac{π}{2} erfi (x) + C

Solution steps

\int x e^{x} d x

Apply Integration By Parts

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

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

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

= e^{x} x - \frac{π}{2} erfi (x)

Add a constant to the solution

= e^{x} x - \frac{π}{2} erfi (x) + C

y^{^{''}} - \frac{y ^{^{'}}}{x} = 3 x

\frac{x ^{5}}{5}

y^{^{'}} + 2 y = x e^{- 2 x}

(4 x - 2)^{3} (x^{2} + 1)^{2}

f (x) = \frac{45}{0.01 x ^{2} + 1}

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