What is the integral of sin(3pit) ?

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

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integral of sin(3pit)

\int sin (3 π t) d t

- \frac{1}{3 π} cos (3 π t) + C

Solution steps

\int sin (3 π t) d t

Apply u-substitution

: \int sin (u) \frac{1}{3 π} d u

= \int sin (u) \frac{1}{3 π} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3 π} (- cos (u))

Substitute back

u = 3 π t

= \frac{1}{3 π} (- cos (3 π t))

Simplify

= - \frac{1}{3 π} cos (3 π t)

Add a constant to the solution

= - \frac{1}{3 π} cos (3 π t) + C

\int \frac{1}{5 - 2 x} d x

6 x - 4 x^{3} + 9

\frac{d}{d x} (t sin (x))

k = 1 \sum \infty e^{- k^{2}}

\frac{\partial}{\partial x} (x^{2} + y^{2} + x y)

What is the integral of sin(3pit) ?
The integral of sin(3pit) is -1/(3pi)cos(3pit)+C