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

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

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integral of cos((npix)/l)

\int cos (\frac{nπ x}{l}) d x

\frac{1}{πn} l sin (\frac{nπ x}{l}) + C

Solution steps

\int cos (\frac{nπ x}{l}) d x

Apply u-substitution

: \int \frac{cos ( \frac{u}{l} )}{πn} d u

= \int \frac{cos ( \frac{u}{l} )}{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 (\frac{u}{l}) d u

Apply u-substitution

: \int cos (v) l d v

= \frac{1}{πn} \cdot \int cos (v) l d v

Take the constant out:

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

= \frac{1}{πn} l \cdot \int cos (v) d v

Use the common integral:

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

= \frac{1}{πn} l sin (v)

Substitute back

= \frac{1}{πn} l sin (\frac{nπ x}{l})

Add a constant to the solution

= \frac{1}{πn} l sin (\frac{nπ x}{l}) + C

x \to 1 lim (4 - x)

\int 4 tan^{3} (x) d x

y^{^{'}} + \frac{6}{5} y = 1 - \frac{1}{6} t

f (x) = (x^{3} - 8)^{\frac{2}{3}}

y^{^{''}} + 81 y = cos (8 t)

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