Integral of cos(1/x) dx: Solution

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In summary, the integral of cos(1/x) dx is not defined in terms of elementary functions and can only be expressed in terms of special functions. Its domain is all real numbers except for x=0, and there is no known closed form solution for it. It can be evaluated numerically using various methods, and its graph is a non-elementary function that oscillates between positive and negative values with infinitely many oscillations as x approaches 0.
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Emmanuel_Euler
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what is the integral of cos(1/x) dx ??
 
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thank for help (delta)
 
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You have posted a number of these "What is the integral of ... ". Do you understand that very few function can be integrated in terms of elementary functions?
 

FAQ: Integral of cos(1/x) dx: Solution

What is the integral of cos(1/x) dx?

The integral of cos(1/x) dx is not defined in terms of elementary functions. It can only be expressed in terms of special functions such as the Fresnel integral or the Dawson function.

What is the domain of the integral of cos(1/x) dx?

The domain of the integral of cos(1/x) dx is all real numbers except for x = 0, as the function is undefined at x = 0.

Is there a closed form solution for the integral of cos(1/x) dx?

No, there is no known closed form solution for the integral of cos(1/x) dx. It can only be expressed in terms of special functions.

How can the integral of cos(1/x) dx be evaluated numerically?

The integral of cos(1/x) dx can be evaluated numerically using various numerical integration methods such as Simpson's rule, Gaussian quadrature, or Monte Carlo integration.

What is the graph of the integral of cos(1/x) dx?

The graph of the integral of cos(1/x) dx is a non-elementary function that cannot be easily visualized. However, it oscillates between positive and negative values, with infinitely many oscillations as x approaches 0 from both sides.

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