What is the integral of sin(1/x) ?

The integral of sin(1/x) is xsin(1/x)-\Ci(1/x)+C

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integral of sin(1/x)

\int sin (\frac{1}{x}) d x

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

Solution steps

\int sin (\frac{1}{x}) d x

Apply Integration By Parts

: x sin (\frac{1}{x}) - \int - \frac{cos ( \frac{1}{x} )}{x} d x

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

\int - \frac{cos ( \frac{1}{x} )}{x} d x = Ci (\frac{1}{x})

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

Add a constant to the solution

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

f (x) = cot^{3} (x)

y = 2 x, y = 3 x - 4, y = 0

x \to 2 lim (\frac{2 x}{3 x + 1})

\frac{\partial}{\partial y} (y^{3} cos (2 x))

\int \frac{x ^{2} - 121}{x} d x

What is the integral of sin(1/x) ?
The integral of sin(1/x) is xsin(1/x)-\Ci(1/x)+C