What is the integral of xcos(x)y ?

The integral of xcos(x)y is x/2 y^2cos(x)+C

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integral of xcos(x)y

\int x cos (x) y d y

\frac{x}{2} y^{2} cos (x) + C

Solution steps

\int x cos (x) y d y

Take the constant out:

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

= cos (x) x \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= cos (x) x \frac{y ^{2}}{2}

Simplify

cos (x) x \frac{y ^{2}}{2} : \frac{x}{2} y^{2} cos (x)

= \frac{x}{2} y^{2} cos (x)

Add a constant to the solution

= \frac{x}{2} y^{2} cos (x) + C

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