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

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

integral of 3cos(3x)

\int 3 cos (3 x) d x

sin (3 x) + C

Solution steps

\int 3 cos (3 x) d x

Take the constant out:

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

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

Apply u-substitution

= 3 \cdot \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{3} sin (u)

Substitute back

u = 3 x

= 3 \cdot \frac{1}{3} sin (3 x)

Simplify

3 \cdot \frac{1}{3} sin (3 x) : sin (3 x)

= sin (3 x)

Add a constant to the solution

= sin (3 x) + C

t an g e n t f (x) = 5 e^{x} + 7 x, at x = 0

\frac{\partial}{\partial t} (e^{2 x} - x cos (t))

x \to 0.9 lim (x^{2} - 1)

t an g e n t y = 13 x e^{x}

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