What is the integral of cos((npix)/7) ?

The integral of cos((npix)/7) is 7/(pin)sin((pinx)/7)+C

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integral of cos((npix)/7)

\int cos (\frac{nπ x}{7}) d x

\frac{7}{πn} sin (\frac{πn x}{7}) + C

Solution steps

\int cos (\frac{nπ x}{7}) d x

Apply Integration By Parts

: x cos (\frac{πn x}{7}) - \int - \frac{πn}{7} x sin (\frac{πn x}{7}) d x

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

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

= x cos (\frac{πn x}{7}) - (x cos (\frac{πn x}{7}) - \frac{7}{πn} sin (\frac{πn x}{7}))

Simplify

= \frac{7}{πn} sin (\frac{πn x}{7})

Add a constant to the solution

= \frac{7}{πn} sin (\frac{πn x}{7}) + C

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What is the integral of cos((npix)/7) ?
The integral of cos((npix)/7) is 7/(pin)sin((pinx)/7)+C