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

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

Popular >

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

Take the constant out:

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

= - \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

\frac{d}{d x} (ln (2 x^{2}))

\int 9 (x + 7)^{2} ln (x + 7) d x

\int \frac{7 x + 6}{x ^{9}} d x

\int \frac{x ^{3} - x}{( x ^{4} - 2 x ^{2} + 3 ) ^{2}} d x

\int 2 t^{- 4} d t