What is the integral of pi/(10)sin((pix)/5) ?

The integral of pi/(10)sin((pix)/5) is -1/2 cos((pix)/5)+C

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integral of pi/(10)sin((pix)/5)

\int \frac{π}{10} sin (\frac{π x}{5}) d x

- \frac{1}{2} cos (\frac{π x}{5}) + C

Solution steps

\int \frac{π}{10} sin (\frac{π x}{5}) d x

Take the constant out:

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

= \frac{π}{10} \cdot \int sin (\frac{π x}{5}) d x

Apply u-substitution

: \int sin (u) \frac{5}{π} d u

= \frac{π}{10} \cdot \int sin (u) \frac{5}{π} d u

Take the constant out:

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

= \frac{π}{10} \cdot \frac{5}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{π}{10} \cdot \frac{5}{π} (- cos (u))

Substitute back

u = \frac{π x}{5}

= \frac{π}{10} \cdot \frac{5}{π} (- cos (\frac{π x}{5}))

Simplify

\frac{π}{10} \cdot \frac{5}{π} (- cos (\frac{π x}{5})) : - \frac{1}{2} cos (\frac{π x}{5})

= - \frac{1}{2} cos (\frac{π x}{5})

Add a constant to the solution

= - \frac{1}{2} cos (\frac{π x}{5}) + C

\int (7 - x) d x

\int_{0}^{1} \frac{58}{4 y - 1} d y

\frac{d y}{d x} = \frac{x y}{2}

\int \frac{2 x ^{3} + 11 x + 8}{x ^{3} + 4 x ^{2} + 4 x} d x

y^{^{''''}} + 17 y^{^{''}} + 16 y = 0

What is the integral of pi/(10)sin((pix)/5) ?
The integral of pi/(10)sin((pix)/5) is -1/2 cos((pix)/5)+C