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

The integral of xsqrt(e^x) is 2e^{x/2}x-4e^{x/2}+C

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integral of xsqrt(e^x)

\int x e^{x} d x

2 e^{\frac{x}{2}} x - 4 e^{\frac{x}{2}} + C

Solution steps

\int x e^{x} d x

Apply Integration By Parts

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

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

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

= 2 e^{\frac{x}{2}} x - 4 e^{\frac{x}{2}}

Add a constant to the solution

= 2 e^{\frac{x}{2}} x - 4 e^{\frac{x}{2}} + C

t \to 0 lim (- 1)

\frac{d x}{d t} - (tan (t)) x = sin (t), x (0) = 1

\frac{d}{d x} (x^{3} e^{- x^{2}})

\frac{d}{d x} ((5 x + 3)^{2})

y^{^{'}} + y = x e^{- x} + 1

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