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

The integral of cos(y)-sin(x)sin(y) is sin(y)+sin(x)cos(y)+C

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integral of cos(y)-sin(x)sin(y)

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

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

Solution steps

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

Apply the Sum Rule:

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

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{x ^{2}}{( 1 + x ^{4} )} d x

\int (6 - x)^{\frac{1}{2}} d x

\int x^{\frac{8}{5}} d x

\int \frac{2 x - 1}{x ^{2} - 7 x + 10} d x

\int x^{3} arccot (x^{2}) d x

What is the integral of cos(y)-sin(x)sin(y) ?
The integral of cos(y)-sin(x)sin(y) is sin(y)+sin(x)cos(y)+C