What is the integral of (-x^2cos(y)sin(y)-xcos(y)) ?

The integral of (-x^2cos(y)sin(y)-xcos(y)) is -xsin(y)-(x^2)/2 sin^2(y)+C

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integral of (-x^2cos(y)sin(y)-xcos(y))

\int (- x^{2} cos (y) sin (y) - x cos (y)) d y

- x sin (y) - \frac{x ^{2}}{2} sin^{2} (y) + C

Solution steps

\int - x^{2} cos (y) sin (y) - x cos (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) x d y - \int cos (y) sin (y) x^{2} d y

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

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

= - x sin (y) - \frac{x ^{2}}{2} sin^{2} (y)

Add a constant to the solution

= - x sin (y) - \frac{x ^{2}}{2} sin^{2} (y) + C

What is the integral of (-x^2cos(y)sin(y)-xcos(y)) ?
The integral of (-x^2cos(y)sin(y)-xcos(y)) is -xsin(y)-(x^2)/2 sin^2(y)+C