What is the integral of e^{xy}+xye^{xy} ?

The integral of e^{xy}+xye^{xy} is 1/x e^{xy}+e^{xy}y-(e^{xy})/x+C

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integral of e^{xy}+xye^{xy}

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

3 y + x^{4} \frac{d y}{d x} = 2 x y

\int \frac{7 x}{1 - x ^{2}} d x

y = cot (2) (cos (x))

\frac{d}{d x} (5^{x - 1})

G (t) = \frac{4 t}{t + 1}

What is the integral of e^{xy}+xye^{xy} ?
The integral of e^{xy}+xye^{xy} is 1/x e^{xy}+e^{xy}y-(e^{xy})/x+C