What is the integral of cos(3pit) ?

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

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integral of cos(3pit)

\int cos (3 π t) d t

\frac{1}{3 π} sin (3 π t) + C

Solution steps

\int cos (3 π t) d t

Apply u-substitution

: \int cos (u) \frac{1}{3 π} d u

= \int cos (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 cos (u) d u

Use the common integral:

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

= \frac{1}{3 π} sin (u)

Substitute back

u = 3 π t

= \frac{1}{3 π} sin (3 π t)

Add a constant to the solution

= \frac{1}{3 π} sin (3 π t) + C

\int 1 - \frac{3}{y} d y

f (x) = - 8 sin (x)

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3})

x \to 3 lim (2 x - 3)

2 y^{^{''}} + 33 y = 0

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