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

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

Popular >

integral of 3cos(3t)

\int 3 cos (3 t) d t

sin (3 t) + C

Solution steps

\int 3 cos (3 t) d t

Take the constant out:

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

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

Apply u-substitution

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

= 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 t

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

Simplify

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

= sin (3 t)

Add a constant to the solution

= sin (3 t) + C

x \to 2 lim (\frac{2 x - 3}{x + 1})

(3, 1), (- 2, - 2)

n = 0 \sum \infty (n x)^{n}

\int \frac{4}{3} x^{3} d x

y = x^{2}, y = 2 x + 6