What is the integral of cos(npix) ?

The integral of cos(npix) is 1/(pin)sin(npix)+C

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integral of cos(npix)

\int cos (nπ x) d x

\frac{1}{πn} sin (nπ x) + C

Solution steps

\int cos (nπ x) d x

Apply u-substitution

: \int \frac{cos ( u )}{πn} d u

= \int \frac{cos ( u )}{πn} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{πn} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{πn} sin (u)

Substitute back

u = nπ x

= \frac{1}{πn} sin (nπ x)

Add a constant to the solution

= \frac{1}{πn} sin (nπ x) + C

\frac{d}{d x} (arccos (\frac{1 - x ^{2}}{1 + x ^{2}}))

x (x - 1)

y^{^{'}} = (x + 1)^{2}

f (x) = 3 x^{3} - 3 x, (1, 0)

\int sin (2) (π x) cos (5) (π x) d x

What is the integral of cos(npix) ?
The integral of cos(npix) is 1/(pin)sin(npix)+C