What is the integral of (3pi)/2 cos((3pix)/2) ?

The integral of (3pi)/2 cos((3pix)/2) is sin((3pix)/2)+C

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integral of (3pi)/2 cos((3pix)/2)

\int \frac{3 π}{2} cos (\frac{3 π x}{2}) d x

sin (\frac{3 π x}{2}) + C

Solution steps

\int \frac{3 π}{2} cos (\frac{3 π x}{2}) d x

Take the constant out:

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

= \frac{3 π}{2} \cdot \int cos (\frac{3 π x}{2}) d x

Apply u-substitution

: \int cos (u) \frac{2}{3 π} d u

= \frac{3 π}{2} \cdot \int cos (u) \frac{2}{3 π} d u

Take the constant out:

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

= \frac{3 π}{2} \cdot \frac{2}{3 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{3 π}{2} \cdot \frac{2}{3 π} sin (u)

Substitute back

u = \frac{3 x π}{2}

= \frac{3 π}{2} \cdot \frac{2}{3 π} sin (\frac{3 x π}{2})

Simplify

\frac{3 π}{2} \cdot \frac{2}{3 π} sin (\frac{3 x π}{2}) : sin (\frac{3 π x}{2})

= sin (\frac{3 π x}{2})

Add a constant to the solution

= sin (\frac{3 π x}{2}) + C

\frac{d}{d x} (arcsec (3 x + 2))

x \to \frac{7 π}{2} - lim (sec (x))

f (x) = \frac{2 x}{3 - 4 x ^{3}}, at x = \frac{1}{2}

\frac{\partial}{\partial x} (\frac{2}{1 - 3 x ^{3}})

\frac{d y}{d x} = x y + 12 x

What is the integral of (3pi)/2 cos((3pix)/2) ?
The integral of (3pi)/2 cos((3pix)/2) is sin((3pix)/2)+C