What is the integral of (xsin(y)) ?

The integral of (xsin(y)) is -xcos(y)+C

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integral of (xsin(y))

\int (x sin (y)) d y

- x cos (y) + C

Solution steps

\int x sin (y) d y

Take the constant out:

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

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

Use the common integral:

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

= x (- cos (y))

Simplify

= - x cos (y)

Add a constant to the solution

= - x cos (y) + C

x \to - 5 lim (\frac{8}{( x + 5 ) ^{6}})

f (x) = 5 e^{e}

y^{^{'}} = (x + y + 1)^{2}, y (0) = 0

\frac{1}{x + 2}, 1

\frac{d y}{d x} = \frac{( 1 + x )}{x y ^{10}}