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

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

integral of 3cos(x/3)

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

9 sin (\frac{x}{3}) + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

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

= 3 \cdot 3 sin (u)

Substitute back

u = \frac{x}{3}

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

Simplify

= 9 sin (\frac{x}{3})

Add a constant to the solution

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

\frac{d}{d x} (4 x e^{4 x})

x \to 0 - lim (x^{2} - \frac{7}{x})

\int 4 (x - 1) in (x - 1) d x

f (x) = \frac{x cos ( π x ) + 1}{x - 1}

t an g e n t (3 x + 13)^{\frac{1}{2}}