What is the integral of sin(6pit) ?

The integral of sin(6pit) is -1/(6pi)cos(6pit)+C

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integral of sin(6pit)

\int sin (6 π t) d t

- \frac{1}{6 π} cos (6 π t) + C

Solution steps

\int sin (6 π t) d t

Apply u-substitution

: \int sin (u) \frac{1}{6 π} d u

= \int sin (u) \frac{1}{6 π} d u

Take the constant out:

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

= \frac{1}{6 π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{6 π} (- cos (u))

Substitute back

u = 6 π t

= \frac{1}{6 π} (- cos (6 π t))

Simplify

= - \frac{1}{6 π} cos (6 π t)

Add a constant to the solution

= - \frac{1}{6 π} cos (6 π t) + C

y = x - x^{3}, (1, 0)

\int 1 + tan (x) d x

\frac{d}{d x} (5 - 5 cos (x))

\frac{d}{d x} (\frac{1}{( x ^{2} + 1 ) ^{4}})

What is the integral of sin(6pit) ?
The integral of sin(6pit) is -1/(6pi)cos(6pit)+C