What is the integral of 2xcos(y)-ycos(x) ?

The integral of 2xcos(y)-ycos(x) is -ysin(x)+x^2cos(y)+C

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integral of 2xcos(y)-ycos(x)

\int 2 x cos (y) - y cos (x) d x

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

Solution steps

\int 2 x cos (y) - y cos (x) 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 cos (x) y d x + \int 2 cos (y) x d x

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

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

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

Add a constant to the solution

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

\int \frac{5 x}{2} d x

\int x sin (\frac{1}{11}) x d x

\int \frac{20 e ^{0.02 x}}{1 + e ^{0.02 x}} d x

\int x (5 x - 3) d x

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

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