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

\int (\frac{3}{2 x - 1} + \frac{5}{3 x - 4}) d x

\int (4 x^{2} + 3 + \frac{8}{x ^{2} + 1}) d x

\int - \frac{x}{1 + x ^{2}} d x

\int 2 - 3 x^{2} d x

\int \frac{x + 2}{x ^{2} + 2 x + 1} d x

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