What is the integral of xe^{yx} ?

The integral of xe^{yx} is e^{yx} 1/y x-e^{yx} 1/(y^2)+C

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integral of xe^{yx}

\int x e^{y x} d x

e^{y x} \frac{1}{y} x - e^{y x} \frac{1}{y ^{2}} + C

Solution steps

\int x e^{y x} d x

Apply Integration By Parts

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

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

\int e^{y x} \frac{1}{y} d x = e^{y x} \frac{1}{y ^{2}}

= e^{y x} \frac{1}{y} x - e^{y x} \frac{1}{y ^{2}}

Add a constant to the solution

= e^{y x} \frac{1}{y} x - e^{y x} \frac{1}{y ^{2}} + C

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What is the integral of xe^{yx} ?
The integral of xe^{yx} is e^{yx} 1/y x-e^{yx} 1/(y^2)+C