What is the integral of ycos(y) ?

The integral of ycos(y) is ysin(y)+cos(y)+C

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integral of ycos(y)

\int y cos (y) d y

y sin (y) + cos (y) + C

Solution steps

\int y cos (y) d y

Apply Integration By Parts

: y sin (y) - \int sin (y) d y

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

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

= y sin (y) - (- cos (y))

Simplify

= y sin (y) + cos (y)

Add a constant to the solution

= y sin (y) + cos (y) + C

(- \frac{1}{2}, 7), (1, - 1)

e^{- y} cos (x) + \frac{d y}{d x} sin^{2} (x) = 0

\frac{d}{d x} (x^{4} (x + 2)^{3})

\frac{d}{d x} (arccos (\frac{1}{x}))

\frac{d}{d x} ((4 x - 3)^{2 x + 1})