What is the integral of ycos(x)y ?

The integral of ycos(x)y is y^2sin(x)+C

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integral of ycos(x)y

\int y cos (x) y d x

y^{2} sin (x) + C

Solution steps

\int y cos (x) y d x

Take the constant out:

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

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

Simplify

yy : y^{2}

= y^{2} \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= y^{2} sin (x)

Add a constant to the solution

= y^{2} sin (x) + C