What is the integral of (1+y+e^y) ?

The integral of (1+y+e^y) is y+(y^2)/2+e^y+C

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integral of (1+y+e^y)

\int (1 + y + e^{y}) d y

y + \frac{y ^{2}}{2} + e^{y} + C

Solution steps

\int 1 + y + e^{y} d y

Apply the Sum Rule:

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

= \int 1 d y + \int y d y + \int e^{y} d y

\int 1 d y = y

\int y d y = \frac{y ^{2}}{2}

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

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

Add a constant to the solution

= y + \frac{y ^{2}}{2} + e^{y} + C

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What is the integral of (1+y+e^y) ?
The integral of (1+y+e^y) is y+(y^2)/2+e^y+C