What is the integral of sin(2xy) ?

The integral of sin(2xy) is -1/(2y)cos(2yx)+C

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integral of sin(2xy)

\int sin (2 x y) d x

- \frac{1}{2 y} cos (2 y x) + C

Solution steps

\int sin (2 x y) d x

Apply u-substitution

: \int \frac{sin ( u )}{2 y} d u

= \int \frac{sin ( u )}{2 y} d u

Take the constant out:

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

= \frac{1}{2 y} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2 y} (- cos (u))

Substitute back

u = 2 y x

= \frac{1}{2 y} (- cos (2 y x))

Simplify

= - \frac{1}{2 y} cos (2 y x)

Add a constant to the solution

= - \frac{1}{2 y} cos (2 y x) + C

\frac{\partial}{\partial z} (x^{2} yz + \frac{1}{x y z ^{2}})

\int \frac{1}{25 x ^{2} + 2} d x

2 x y y^{^{'}} = 3 y^{2} + x^{2}

\int \frac{e ^{x}}{( e ^{x} - 4 ) ( e ^{2 x} + 1 )} d x

What is the integral of sin(2xy) ?
The integral of sin(2xy) is -1/(2y)cos(2yx)+C