What is the integral of xe^{2y} ?

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

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integral of xe^{2y}

\int x e^{2 y} d x

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

Solution steps

\int x e^{2 y} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2 y} \cdot \int x d x

Apply the Power Rule

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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