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

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

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integral of cos((pix)/2)+picos(x)

\int cos (\frac{π x}{2}) + π cos (x) d x

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

Solution steps

\int cos (\frac{π x}{2}) + π 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 cos (\frac{π x}{2}) d x + \int π cos (x) d x

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

\int π cos (x) d x = π sin (x)

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

Add a constant to the solution

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

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