What is the integral of sin(5pit) ?

The integral of sin(5pit) is -1/(5pi)cos(5pit)+C

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integral of sin(5pit)

\int sin (5 π t) d t

- \frac{1}{5 π} cos (5 π t) + C

Solution steps

\int sin (5 π t) d t

Apply u-substitution

: \int sin (u) \frac{1}{5 π} d u

= \int sin (u) \frac{1}{5 π} d u

Take the constant out:

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

= \frac{1}{5 π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{5 π} (- cos (u))

Substitute back

u = 5 π t

= \frac{1}{5 π} (- cos (5 π t))

Simplify

= - \frac{1}{5 π} cos (5 π t)

Add a constant to the solution

= - \frac{1}{5 π} cos (5 π t) + C

\frac{d}{d x} (3 x + \frac{5}{x})

\frac{d y}{d x} = \frac{10 x}{7 y}

\frac{d}{d t} (1 + t^{3})

- 3 cot (x)

\int \frac{x}{x + 5} d x

What is the integral of sin(5pit) ?
The integral of sin(5pit) is -1/(5pi)cos(5pit)+C