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

The integral of (sin(3t)) is -1/3 cos(3t)+C

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integral of (sin(3t))

\int (sin (3 t)) d t

- \frac{1}{3} cos (3 t) + C

Solution steps

\int sin (3 t) d t

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3} (- cos (u))

Substitute back

u = 3 t

= \frac{1}{3} (- cos (3 t))

Simplify

= - \frac{1}{3} cos (3 t)

Add a constant to the solution

= - \frac{1}{3} cos (3 t) + C

(1.4) (7.1)

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{2}} d x

f (x) = \frac{1 - 4 x}{3 + x}

x \to 5 lim (ln (x - 4) + \frac{1}{2})

\int n o n e d x