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

The integral of 2+2cos(x) is 2x+2sin(x)+C

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integral of 2+2cos(x)

\int 2 + 2 cos (x) d x

2 x + 2 sin (x) + C

Solution steps

\int 2 + 2 cos (x) d x

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

\int 2 d x = 2 x

\int 2 cos (x) d x = 2 sin (x)

= 2 x + 2 sin (x)

Add a constant to the solution

= 2 x + 2 sin (x) + C

\int \frac{1}{3 - 4 x - x ^{2}} d x

d y = (x - 2 y cot (2 x)) d x

x (8 x + 5)^{4}

x^{3} e^{x} cos (x)

\int \frac{2 x + 4}{x ^{2} - 2 x - 3} d x