What is the integral of cos((npi)/2 x) ?

The integral of cos((npi)/2 x) is 2/(pin)sin((npi)/2 x)+C

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integral of cos((npi)/2 x)

\int cos (\frac{nπ}{2} x) d x

\frac{2}{πn} sin (\frac{nπ}{2} x) + C

Solution steps

\int cos (\frac{nπ}{2} x) d x

Apply u-substitution

: \int \frac{2 cos ( u )}{πn} d u

= \int \frac{2 cos ( u )}{πn} d u

Take the constant out:

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

= \frac{2}{πn} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{πn} sin (u)

Substitute back

u = \frac{nπ}{2} x

= \frac{2}{πn} sin (\frac{nπ}{2} x)

Add a constant to the solution

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

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} - 2 x})

x \to 1 lim (sin (\frac{1}{x}))

\int (x^{2} \cdot sin (x)) d x

\frac{d}{d x} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

\frac{d}{d x} (- tan (x^{2}))

What is the integral of cos((npi)/2 x) ?
The integral of cos((npi)/2 x) is 2/(pin)sin((npi)/2 x)+C