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

(6 + x) y^{^{'}} = 7 y

\int \frac{3}{18 + 2 t ^{2}} d t

\frac{d}{d x} (cos (t) i)

x \to 1 lim (30)

\int \frac{1}{5 - 6 x} d x

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