What is the integral from 0 to 5 of y+xe^y ?

The integral from 0 to 5 of y+xe^y is 5y+e^y 25/2

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integral from 0 to 5 of y+xe^y

\int_{0}^{5} y + x e^{y} d x

5 y + e^{y} \frac{25}{2}

Solution steps

\int_{0}^{5} y + x e^{y} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} y d x + \int_{0}^{5} e^{y} x d x

\int_{0}^{5} y d x = 5 y

\int_{0}^{5} e^{y} x d x = e^{y} \frac{25}{2}

= 5 y + e^{y} \frac{25}{2}

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What is the integral from 0 to 5 of y+xe^y ?
The integral from 0 to 5 of y+xe^y is 5y+e^y 25/2