What is the integral of 3sin(x/3) ?

The integral of 3sin(x/3) is -9cos(x/3)+C

Popular >

integral of 3sin(x/3)

\int 3 sin (\frac{x}{3}) d x

- 9 cos (\frac{x}{3}) + C

Solution steps

\int 3 sin (\frac{x}{3}) d x

Take the constant out:

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

= 3 \cdot \int sin (\frac{x}{3}) d x

Apply u-substitution

: \int sin (u) \cdot 3 d u

= 3 \cdot \int sin (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot 3 \cdot \int sin (u) d u

Use the common integral:

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

= 3 \cdot 3 (- cos (u))

Substitute back

u = \frac{x}{3}

= 3 \cdot 3 (- cos (\frac{x}{3}))

Simplify

= - 9 cos (\frac{x}{3})

Add a constant to the solution

= - 9 cos (\frac{x}{3}) + C

\int (x^{2} - 3) e^{x} d x

\frac{d}{d x} ((2 x^{2} + x)^{200})

f (x) = \frac{y - 1}{3}

\frac{d}{d x} (\frac{5}{x} ln (x))

(tan (3 x))^{^{'}}