What is the integral of (xe^{2y})/(4-y) ?

The integral of (xe^{2y})/(4-y) is (e^{2y}}{4-y}*\frac{x^2)/2+C

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integral of (xe^{2y})/(4-y)

\int \frac{x e ^{2 y}}{4 - y} d x

\frac{e ^{2 y}}{4 - y} \cdot \frac{x ^{2}}{2} + C

Solution steps

\int \frac{x e ^{2 y}}{4 - y} d x

Take the constant out:

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

= \frac{e ^{2 y}}{4 - y} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{e ^{2 y}}{4 - y} \cdot \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{e ^{2 y}}{4 - y} \cdot \frac{x ^{2}}{2} + C

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What is the integral of (xe^{2y})/(4-y) ?
The integral of (xe^{2y})/(4-y) is (e^{2y}}{4-y}*\frac{x^2)/2+C