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 \cdot 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

2 sin (t) cos (t)

y^{^{''}} - 4 y^{^{'}} + 5 = 0

f (x) = \frac{5}{2 5 x + 6}, at a = 2

y = \frac{x ^{3}}{9}, 0 \leq x \leq 2

t y^{^{'}} + 7 y = t^{2} - t + 1, y (1) = \frac{1}{7}

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