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

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

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integral of cos(pix)+2

\int cos (π x) + 2 d x

\frac{1}{π} sin (π x) + 2 x + C

Solution steps

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

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

\int 2 d x = 2 x

= \frac{1}{π} sin (π x) + 2 x

Add a constant to the solution

= \frac{1}{π} sin (π x) + 2 x + C

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