What is the integral of sin(y)-ysin(x) ?

The integral of sin(y)-ysin(x) is xsin(y)+ycos(x)+C

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integral of sin(y)-ysin(x)

\int sin (y) - y sin (x) d x

x sin (y) + y cos (x) + C

Solution steps

\int sin (y) - y sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= sin (y) x - (- y cos (x))

Simplify

= x sin (y) + y cos (x)

Add a constant to the solution

= x sin (y) + y cos (x) + C

\frac{\partial}{\partial x} (e^{x y^{2}} + 4 z y^{3})

(1 + x^{2}) \frac{d y}{d x} + x y = 0

y = x^{- \frac{1}{2}}

\frac{d}{d x} (x^{2} \cdot y^{2})

\int \frac{1}{9 - 16 x ^{2}} d x

What is the integral of sin(y)-ysin(x) ?
The integral of sin(y)-ysin(x) is xsin(y)+ycos(x)+C