What is the integral of cos(pi*x) ?

The integral of cos(pi*x) is 1/pi sin(pix)+C

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integral of cos(pi*x)

\int cos (π \cdot x) d x

\frac{1}{π} sin (π x) + C

Solution steps

\int cos (π x) d x

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 x

= \frac{1}{π} sin (π x)

Add a constant to the solution

= \frac{1}{π} sin (π x) + C

f (x) = x^{4} - 5 x^{2} + 4, at x = - 2

y = sin (3) x^{2}

\int (ln (x) + x) d x

\frac{1}{( ( 25 s ^{2} + 19980 ) )}

\frac{\partial}{\partial x} (\frac{1}{x} sin (\frac{y}{x}))

What is the integral of cos(pi*x) ?
The integral of cos(pi*x) is 1/pi sin(pix)+C