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

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

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integral of cos((nx)/2)

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

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

Solution steps

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

Apply u-substitution

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

= \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

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

Use the common integral:

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

= \frac{2}{n} sin (u)

Substitute back

u = \frac{n x}{2}

= \frac{2}{n} sin (\frac{n x}{2})

Add a constant to the solution

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

\int \frac{1}{( 1 + e ^{- y} )} d y

\int x^{7} e^{- x^{4}} d x

\int lo g_{b} (x) d x

y + x = 4, 36 - 9 x = y^{2}

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