What is the integral of 1+ye^{(xy)} ?

The integral of 1+ye^{(xy)} is x+e^{yx}+C

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integral of 1+ye^{(xy)}

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

x + e^{y x} + C

Solution steps

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

\int 1 d x = x

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

= x + e^{y x}

Add a constant to the solution

= x + e^{y x} + C

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