What is the integral of sin((xy)/2) ?

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

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integral of sin((xy)/2)

\int sin (\frac{x y}{2}) d y

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

Solution steps

\int sin (\frac{x y}{2}) d y

Rewrite using trig identities

= \int 1 - cos (y x) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d y - \int cos (y x) d y

\int 1 d y = y

\int cos (y x) d y = \frac{1}{x} sin (y x)

= y - \frac{1}{x} sin (y x)

Add a constant to the solution

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

x \to 0 lim (\frac{cos ( x )}{5 x})

\frac{d}{d t} (3 cos (2 t))

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

x \to 1 lim (4 x - 1)

\frac{d}{d x} (100 x^{2} - 26 x e^{x})

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