What is the integral of xe^{1/2 x} ?

The integral of xe^{1/2 x} is 2e^{1/2 x}x-4e^{1/2 x}+C

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integral of xe^{1/2 x}

\int x e^{\frac{1}{2} x} d x

2 e^{\frac{1}{2} x} x - 4 e^{\frac{1}{2} x} + C

Solution steps

\int x e^{\frac{1}{2} x} d x

Apply Integration By Parts

: 2 e^{\frac{1}{2} x} x - \int 2 e^{\frac{1}{2} x} d x

= 2 e^{\frac{1}{2} x} x - \int 2 e^{\frac{1}{2} x} d x

\int 2 e^{\frac{1}{2} x} d x = 4 e^{\frac{1}{2} x}

= 2 e^{\frac{1}{2} x} x - 4 e^{\frac{1}{2} x}

Add a constant to the solution

= 2 e^{\frac{1}{2} x} x - 4 e^{\frac{1}{2} x} + C

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What is the integral of xe^{1/2 x} ?
The integral of xe^{1/2 x} is 2e^{1/2 x}x-4e^{1/2 x}+C