What is the integral of sin(pi/4 x) ?

The integral of sin(pi/4 x) is -4/pi cos(pi/4 x)+C

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integral of sin(pi/4 x)

\int sin (\frac{π}{4} x) d x

- \frac{4}{π} cos (\frac{π}{4} x) + C

Solution steps

\int sin (\frac{π}{4} x) d x

Apply u-substitution

: \int sin (u) \frac{4}{π} d u

= \int sin (u) \frac{4}{π} d u

Take the constant out:

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

= \frac{4}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{4}{π} (- cos (u))

Substitute back

u = \frac{π}{4} x

= \frac{4}{π} (- cos (\frac{π}{4} x))

Simplify

= - \frac{4}{π} cos (\frac{π}{4} x)

Add a constant to the solution

= - \frac{4}{π} cos (\frac{π}{4} x) + C

\int (1 + 3 x) x^{2} d x

sin (x y^{2})

\frac{d}{d x} (\frac{1458}{( 1 + 9 x ) ^{3}})

\int \frac{2 25 + e ^{8 x}}{e ^{4 x}} d x

x \to - 3 lim (\frac{x ^{3} + 27}{x ^{2} + 13 x + 30})

What is the integral of sin(pi/4 x) ?
The integral of sin(pi/4 x) is -4/pi cos(pi/4 x)+C