What is the integral of pisin(nx) ?

The integral of pisin(nx) is -pi/n cos(nx)+C

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integral of pisin(nx)

\int π sin (n x) d x

- \frac{π}{n} cos (n x) + C

Solution steps

\int π sin (n x) d x

Take the constant out:

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

= π \cdot \int sin (n x) d x

Apply u-substitution

: \int \frac{sin ( u )}{n} d u

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

Take the constant out:

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

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

Use the common integral:

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

= π \frac{1}{n} (- cos (u))

Substitute back

u = n x

= π \frac{1}{n} (- cos (n x))

Simplify

π \frac{1}{n} (- cos (n x)) : - \frac{π}{n} cos (n x)

= - \frac{π}{n} cos (n x)

Add a constant to the solution

= - \frac{π}{n} cos (n x) + C

\frac{d y}{d x} = \frac{x ^{2}}{( y ( 1 + x ^{2} ) )}

x \to 1 lim ((x - 1) ∣ x - 1 ∣)

x \to 0 - lim (2)

n = 0 \sum \infty \frac{( 2 ^{n} )}{9 ^{2 n + 1}}

\int 2 x^{2} - 3 x + 2 d x

What is the integral of pisin(nx) ?
The integral of pisin(nx) is -pi/n cos(nx)+C