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

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

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integral of cos(x)+xcos(y)-y

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

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

Solution steps

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

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

\int y d y = \frac{y ^{2}}{2}

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (\frac{3 y}{2 x})

f (x) = \frac{x ^{2}}{7 + x}

x y^{^{'}} - 2 y = 2 y x^{2}

\frac{d}{d x} ((x^{2} - 3 x)^{6} (4 - x)^{5})

x \to 2 lim (e^{\frac{1}{x - 2}})

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