What is the integral of 5sin(x/4) ?

The integral of 5sin(x/4) is -20cos(x/4)+C

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integral of 5sin(x/4)

\int 5 sin (\frac{x}{4}) d x

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

Solution steps

\int 5 sin (\frac{x}{4}) d x

Take the constant out:

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

= 5 \cdot \int sin (\frac{x}{4}) d x

Apply u-substitution

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

= 5 \cdot \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

= 5 \cdot 4 \cdot \int sin (u) d u

Use the common integral:

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

= 5 \cdot 4 (- cos (u))

Substitute back

u = \frac{x}{4}

= 5 \cdot 4 (- cos (\frac{x}{4}))

Simplify

= - 20 cos (\frac{x}{4})

Add a constant to the solution

= - 20 cos (\frac{x}{4}) + C

\frac{d}{d s} (\frac{1}{s ^{2}})

4 x^{- \frac{1}{8}}

(\frac{3 x ^{2}}{( 2 x + 4 )})^{3}

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

y = x^{2}, (2, 4)