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

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

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integral of (1+xy)e^{xy}

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

e^{y x} x + C

Solution steps

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

Apply Integration By Parts

: e^{y x} \frac{1}{y} + e^{y x} x - \int e^{y x} d x

= e^{y x} \frac{1}{y} + e^{y x} x - \int e^{y x} d x

\int e^{y x} d x = \frac{1}{y} e^{y x}

= e^{y x} \frac{1}{y} + e^{y x} x - \frac{1}{y} e^{y x}

Simplify

= e^{y x} x

Add a constant to the solution

= e^{y x} x + C

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