What is the integral of sin(x/5) ?

The integral of sin(x/5) is -5cos(x/5)+C

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integral of sin(x/5)

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

- 5 cos (\frac{x}{5}) + C

Solution steps

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

Apply u-substitution

: \int sin (u) \cdot 5 d u

= \int sin (u) \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int sin (u) d u

Use the common integral:

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

= 5 (- cos (u))

Substitute back

u = \frac{x}{5}

= 5 (- cos (\frac{x}{5}))

Simplify

= - 5 cos (\frac{x}{5})

Add a constant to the solution

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

a x^{3}, at x = - 5

y = 3 arctan (x - 1 + x^{2})

\frac{\partial}{\partial y} (y^{3} cos (x + y))

\int (2 x^{3} + 10 x^{2} - 3 x + 4) d x

y^{^{''}} - 6 y^{^{'}} = 4 t