What is the integral of (1+cos(y)) ?

The integral of (1+cos(y)) is y+sin(y)+C

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integral of (1+cos(y))

\int (1 + cos (y)) d y

y + sin (y) + C

Solution steps

\int 1 + cos (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 1 d y + \int cos (y) d y

\int 1 d y = y

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

= y + sin (y)

Add a constant to the solution

= y + sin (y) + C

\frac{π}{6} cos (x)

2 - x^{6}

\int 5 x - x^{2} - x d x

h \to 0 lim (\frac{( 4 + h ) - ( 4 )}{h})

x \frac{d y}{d x} - 2 y = x^{- 2} + 2 x^{3} e^{x}