What is the integral of (sin(pix))/pi ?

The integral of (sin(pix))/pi is -1/(pi^2)cos(pix)+C

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integral of (sin(pix))/pi

\int \frac{sin ( π x )}{π} d x

- \frac{1}{π ^{2}} cos (π x) + C

Solution steps

\int \frac{sin ( π x )}{π} d x

Take the constant out:

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

= \frac{1}{π} \cdot \int sin (π x) d x

Apply u-substitution

: \int sin (u) \frac{1}{π} d u

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

Use the common integral:

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

= \frac{1}{π} \cdot \frac{1}{π} (- cos (u))

Substitute back

u = π x

= \frac{1}{π} \cdot \frac{1}{π} (- cos (π x))

Simplify

\frac{1}{π} \cdot \frac{1}{π} (- cos (π x)) : - \frac{1}{π ^{2}} cos (π x)

= - \frac{1}{π ^{2}} cos (π x)

Add a constant to the solution

= - \frac{1}{π ^{2}} cos (π x) + C

\frac{\partial}{\partial g} (2 π \frac{l}{g})

(t - 1)^{2}

\int e^{4 l n (x)} d x

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

x \to 2 + lim (4 x^{2} - 2 x + 3)

What is the integral of (sin(pix))/pi ?
The integral of (sin(pix))/pi is -1/(pi^2)cos(pix)+C