What is the integral of picos((nx)/2) ?

The integral of picos((nx)/2) is pi 2/n sin((nx)/2)+C

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integral of picos((nx)/2)

\int π cos (\frac{n x}{2}) d x

π \frac{2}{n} sin (\frac{n x}{2}) + C

Solution steps

\int π cos (\frac{n x}{2}) d x

Take the constant out:

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

= π \cdot \int cos (\frac{n x}{2}) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{n} d u

= π \cdot \int \frac{2 cos ( u )}{n} d u

Take the constant out:

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

= π \frac{2}{n} \cdot \int cos (u) d u

Use the common integral:

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

= π \frac{2}{n} sin (u)

Substitute back

u = \frac{n x}{2}

= π \frac{2}{n} sin (\frac{n x}{2})

Add a constant to the solution

= π \frac{2}{n} sin (\frac{n x}{2}) + C

x \to 0 lim (- 7)

\frac{\partial}{\partial x} (e^{- x} cos (π t))

\int \frac{x ^{2} - 1}{x ^{2}} d x

\int \frac{x}{x} d x

\frac{1}{2} x^{3} + 2, x + 1, x = 0, x = 2

What is the integral of picos((nx)/2) ?
The integral of picos((nx)/2) is pi 2/n sin((nx)/2)+C