What is the integral of pisin((pix)/7)+1 ?

The integral of pisin((pix)/7)+1 is -7cos((pix)/7)+x+C

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integral of pisin((pix)/7)+1

\int π sin (\frac{π x}{7}) + 1 d x

- 7 cos (\frac{π x}{7}) + x + C

Solution steps

\int π sin (\frac{π x}{7}) + 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 π sin (\frac{π x}{7}) d x + \int 1 d x

\int π sin (\frac{π x}{7}) d x = - 7 cos (\frac{π x}{7})

\int 1 d x = x

= - 7 cos (\frac{π x}{7}) + x

Add a constant to the solution

= - 7 cos (\frac{π x}{7}) + x + C

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What is the integral of pisin((pix)/7)+1 ?
The integral of pisin((pix)/7)+1 is -7cos((pix)/7)+x+C