What is the integral of cos((npix)/4) ?

The integral of cos((npix)/4) is 4/(pin)sin((pinx)/4)+C

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integral of cos((npix)/4)

\int cos (\frac{nπ x}{4}) d x

\frac{4}{πn} sin (\frac{πn x}{4}) + C

Solution steps

\int cos (\frac{nπ x}{4}) d x

Apply Integration By Parts

= x cos (\frac{πn x}{4}) - \int - \frac{πn}{4} x sin (\frac{πn x}{4}) d x

\int - \frac{πn}{4} x sin (\frac{πn x}{4}) d x = x cos (\frac{πn x}{4}) - \frac{4}{πn} sin (\frac{πn x}{4})

= x cos (\frac{πn x}{4}) - (x cos (\frac{πn x}{4}) - \frac{4}{πn} sin (\frac{πn x}{4}))

Simplify

= \frac{4}{πn} sin (\frac{πn x}{4})

Add a constant to the solution

= \frac{4}{πn} sin (\frac{πn x}{4}) + C

What is the integral of cos((npix)/4) ?
The integral of cos((npix)/4) is 4/(pin)sin((pinx)/4)+C