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

The integral of (xcos(y)) is xsin(y)+C

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integral of (xcos(y))

\int (x cos (y)) d y

x sin (y) + C

Solution steps

\int x cos (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= x sin (y)

Add a constant to the solution

= x sin (y) + C

\frac{\partial}{\partial x} (y - x)

\int \frac{sin ( 2 x )}{cos ( x )} d x

\frac{d y}{d x} = 5 x

\int_{- 2}^{2} x^{2} + 1 d x

\frac{d}{d x} (8 x^{- 1})