What is the integral of 2ye^y ?

The integral of 2ye^y is 2(e^yy-e^y)+C

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integral of 2ye^y

\int 2 y e^{y} d y

2 (e^{y} y - e^{y}) + C

Solution steps

\int 2 y e^{y} d y

Take the constant out:

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

= 2 \cdot \int y e^{y} d y

Apply Integration By Parts

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

= 2 (e^{y} y - \int e^{y} d y)

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

= 2 (e^{y} y - e^{y})

Add a constant to the solution

= 2 (e^{y} y - e^{y}) + C

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