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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int [cos (\frac{x}{2}) - sin (3 \frac{x}{2})] d x

\frac{d}{d x} (\frac{7}{x ^{- 2}} + \frac{5}{x ^{- 3}})

x, \frac{1}{3} x, x = 25

\frac{d}{d x} (arccot (\frac{x}{5}))

x \to 0 lim (\frac{100}{2})

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