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

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

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integral of xcos(y)-2y

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int \frac{3 x - 2}{x ^{2} + 2 x + 4} d x

\int (\frac{3 x ^{2} + 9 x + 1}{x}) d x

\int cot (θ) csc (θ) d θ

\int x + 2 ln (x) d x

\int y \cdot e^{x y} d x

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