What is the integral of-ye^y ?

The integral of-ye^y is -e^yy+e^y+C

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integral of-ye^y

\int - y e^{y} d y

- e^{y} y + e^{y} + C

Solution steps

\int - y e^{y} d y

Take the constant out:

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

= - \int y e^{y} d y

Apply Integration By Parts

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

= - (e^{y} y - \int e^{y} d y)

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

= - (e^{y} y - e^{y})

Simplify

= - e^{y} y + e^{y}

Add a constant to the solution

= - e^{y} y + e^{y} + C

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