What is the integral of cos(pit) ?

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

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integral of cos(pit)

\int cos (π t) d t

\frac{1}{π} sin (π t) + C

Solution steps

\int cos (π t) d t

Apply u-substitution

: \int cos (u) \frac{1}{π} d u

= \int cos (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{π} sin (u)

Substitute back

u = π t

= \frac{1}{π} sin (π t)

Add a constant to the solution

= \frac{1}{π} sin (π t) + C

y = x (27 x^{- 2} + 4)

x \to + 2 + lim (\frac{x}{x - 2})

\int x \cdot e^{- s x} d x

\frac{\partial}{\partial y} (\frac{e ^{y}}{e ^{x} + e ^{y}})

\frac{d}{d x} (3 x^{2} - 2 x + 5)