What is the integral of 2y+cos(y) ?

The integral of 2y+cos(y) is y^2+sin(y)+C

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integral of 2y+cos(y)

\int 2 y + cos (y) d y

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

Solution steps

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

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

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

= y^{2} + sin (y)

Add a constant to the solution

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

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