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Popular Calculus >

integral of 2+x+ye^y

Solution

\int 2 + x + y e^{y} d y

Solution

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

Solution steps

\int 2 + x + 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 2 d y + \int x d y + \int e^{y} y d y

\int 2 d y = 2 y

\int x d y = x y

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

= 2 y + x y + e^{y} y - e^{y}

Add a constant to the solution

= 2 y + x y + e^{y} y - e^{y} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 2+x+ye^y ?
The integral of 2+x+ye^y is 2y+xy+e^yy-e^y+C