What is the integral of ysin(x)y ?

The integral of ysin(x)y is -y^2cos(x)+C

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integral of ysin(x)y

\int y sin (x) y d x

- y^{2} cos (x) + C

Solution steps

\int y sin (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 sin (x) d x

Simplify

yy : y^{2}

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

Use the common integral:

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

= y^{2} (- cos (x))

Simplify

= - y^{2} cos (x)

Add a constant to the solution

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

\int \frac{e ^{x}}{e ^{3 x} - 2 e ^{2 x} + e ^{x} - 2} d x

\frac{\partial}{\partial y} (6 x y^{2})

\int 4 x ln (7 x) d x

\frac{\partial}{\partial x} (ln (2 x + y + 1))

y^{^{'}} + 3 y = 8 x, y (0) = 4