What is the integral of sin(4xy) ?

The integral of sin(4xy) is -1/(4y)cos(4yx)+C

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integral of sin(4xy)

\int sin (4 x y) d x

- \frac{1}{4 y} cos (4 y x) + C

Solution steps

\int sin (4 x y) d x

Apply u-substitution

: \int \frac{sin ( u )}{4 y} d u

= \int \frac{sin ( u )}{4 y} d u

Take the constant out:

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

= \frac{1}{4 y} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{4 y} (- cos (u))

Substitute back

u = 4 y x

= \frac{1}{4 y} (- cos (4 y x))

Simplify

= - \frac{1}{4 y} cos (4 y x)

Add a constant to the solution

= - \frac{1}{4 y} cos (4 y x) + C

(1 - x)^{2}

\frac{d}{d x} (x^{4} (2 x - 5)^{6})

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

x = \frac{1}{12 y}, y = x, x = 16 y

\frac{\partial}{\partial x} (- (\frac{x}{y}))

What is the integral of sin(4xy) ?
The integral of sin(4xy) is -1/(4y)cos(4yx)+C