What is the integral of sin(1/4 x) ?

The integral of sin(1/4 x) is -4cos(1/4 x)+C

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integral of sin(1/4 x)

\int sin (\frac{1}{4} x) d x

- 4 cos (\frac{1}{4} x) + C

Solution steps

\int sin (\frac{1}{4} x) d x

Apply u-substitution

: \int sin (u) \cdot 4 d u

= \int sin (u) \cdot 4 d u

Take the constant out:

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

= 4 \cdot \int sin (u) d u

Use the common integral:

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

= 4 (- cos (u))

Substitute back

u = \frac{1}{4} x

= 4 (- cos (\frac{1}{4} x))

Simplify

= - 4 cos (\frac{1}{4} x)

Add a constant to the solution

= - 4 cos (\frac{1}{4} x) + C

\frac{\partial}{\partial x} ((x - u)^{2})

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

\frac{d}{d x} (e^{- 3 x^{4}} \cdot ln (7 x^{2}))

\frac{\partial}{\partial y} (\frac{x}{y ^{2}})

x \to 0 lim (\frac{7}{1 + x})

What is the integral of sin(1/4 x) ?
The integral of sin(1/4 x) is -4cos(1/4 x)+C