What is the integral of cos(pix-npix) ?

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

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integral of cos(pix-npix)

\int cos (π x - nπ x) d x

\frac{1}{π - πn} sin (π x - nπ x) + C

Solution steps

\int cos (π x - nπ x) d x

Apply u-substitution

: \int \frac{cos ( u )}{π - πn} d u

= \int \frac{cos ( u )}{π - πn} d u

Take the constant out:

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

= \frac{1}{π - πn} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{π - πn} sin (u)

Substitute back

u = π x - nπ x

= \frac{1}{π - πn} sin (π x - nπ x)

Add a constant to the solution

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

y = (2 t - 1) (3 t - 4)^{- 1}

\int \frac{1 + cos ( 2 θ )}{2} d θ

\frac{\partial}{\partial s} (4 s t)

\frac{d y}{d x} = y - 2 x

x \to 4 lim (x - 6)

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