What is the integral of 7sin(x/3) ?

The integral of 7sin(x/3) is -21cos(x/3)+C

Popular >

integral of 7sin(x/3)

\int 7 sin (\frac{x}{3}) d x

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

Solution steps

\int 7 sin (\frac{x}{3}) d x

Take the constant out:

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

= 7 \cdot \int sin (\frac{x}{3}) d x

Apply u-substitution

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

= 7 \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

= 7 \cdot 3 \cdot \int sin (u) d u

Use the common integral:

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

= 7 \cdot 3 (- cos (u))

Substitute back

u = \frac{x}{3}

= 7 \cdot 3 (- cos (\frac{x}{3}))

Simplify

= - 21 cos (\frac{x}{3})

Add a constant to the solution

= - 21 cos (\frac{x}{3}) + C

y^{^{'}} = \frac{x ^{4} y ^{3} + 2 x ^{4}}{y ^{2}}

\frac{d}{d x} (- \frac{1}{8} cos (\frac{x}{2}))

\int \frac{x}{6} e^{x^{2}} d x

\frac{\partial}{\partial x} (sin (7 y^{2} - 7 x y))

\int e^{2 x} (x + 1) d x