What is the integral of cos(2x)+1 ?

The integral of cos(2x)+1 is 1/2 sin(2x)+x+C

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integral of cos(2x)+1

\int cos (2 x) + 1 d x

\frac{1}{2} sin (2 x) + x + C

Solution steps

\int cos (2 x) + 1 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 cos (2 x) d x + \int 1 d x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

\int 1 d x = x

= \frac{1}{2} sin (2 x) + x

Add a constant to the solution

= \frac{1}{2} sin (2 x) + x + C

\int 3 e^{2 t} d t

\int 6 e^{5 x + e^{5 x}} d x

\frac{d}{d y} (- \frac{x}{y})

x \to \infty lim (a x^{2})

What is the integral of cos(2x)+1 ?
The integral of cos(2x)+1 is 1/2 sin(2x)+x+C