What is the integral of cos(2pit) ?

The integral of cos(2pit) is 1/(2pi)sin(2tpi)+C

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integral of cos(2pit)

\int cos (2 π t) d t

\frac{1}{2 π} sin (2 t π) + C

Solution steps

\int cos (2 π t) d t

Apply u-substitution

: \int cos (u) \frac{1}{2 π} d u

= \int cos (u) \frac{1}{2 π} d u

Take the constant out:

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

= \frac{1}{2 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2 π} sin (u)

Substitute back

u = 2 t π

= \frac{1}{2 π} sin (2 t π)

Add a constant to the solution

= \frac{1}{2 π} sin (2 t π) + C

\int \frac{e ^{x}}{9 - e ^{2 x}} d x

\frac{\partial}{\partial u} (u^{5} + v^{7})

\frac{\partial}{\partial x} (y^{2} + 16)

\frac{d}{d x} (\frac{x + 1}{x + 5})

y^{^{''}} - 8 y^{^{'}} + 25 y = 208 sin (3 x)

What is the integral of cos(2pit) ?
The integral of cos(2pit) is 1/(2pi)sin(2tpi)+C