What is the integral of (xe^x)/2 ?

The integral of (xe^x)/2 is 1/2 (e^xx-e^x)+C

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integral of (xe^x)/2

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

\int e^{x} d x = e^{x}

= \frac{1}{2} (e^{x} x - e^{x})

Add a constant to the solution

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

\frac{\partial}{\partial x} (ln (x + 3 y + 7 z))

\int tan^{3} (x) (sec (x))^{\frac{3}{2}} d x

\frac{\partial}{\partial y} (2 y^{2} + 3 x)

x \to 0 lim (\frac{3}{0})

n = 0 \sum \infty (\frac{1}{3})^{2 n}