What is the integral of xysin(z) ?

The integral of xysin(z) is -xycos(z)+C

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integral of xysin(z)

\int x y sin (z) d z

- x y cos (z) + C

Solution steps

\int x y sin (z) d z

Take the constant out:

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

= x y \cdot \int sin (z) d z

Use the common integral:

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

= x y (- cos (z))

Simplify

= - x y cos (z)

Add a constant to the solution

= - x y cos (z) + C

y = x^{- \frac{1}{7}}, (1, 1)

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

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 3) x^{2})

\frac{d}{d x} (- 2 x^{- 3})

g^{'} (x)