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Evaluate the indefinite integral as an infinite series.

$ \int \frac {\cos x - 1}{x} dx $

$c+\sum_{n=1}^{\infty} \frac{(-1)^{n}}{2 n \cdot(2 n) !} x^{2 n}$ where $c$ is a constant.

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the value of the happening in the world as an infinite series. Okay, so we gonna first fun, even serious. The experience because an X minus one over X and this is a cook, and this is just equals two. So we expand a course on the bags is gonna be is its four alpha Kappa Tau Oreo minus six. Always his sartorial and so on. So this minus one over X, the X end is going to be so interchange the order of integral and summation. And this is Kay from zero to infinity. A different one. All right, so minus one is going to be minus. That's swear over tutorial class. It's the four auto tutorial minus six. Always it's Vittorio. And we can calamitous turn and right as a summation. So which is gonna be overact? So it's gonna be minus one hour. Kay xed for two k over to Victorio. Notice what? Exposed to tremendous one. Yeah, this cracked. Okay, so we're gonna anywhere this part, which is because to keep from one's for even a modest wanted public, a over to get territorial and the integral this this part the indefinite acquittal for export to command us wants to be too few minutes export. Who came over to territorial? Oh, I'm sorry. It's not just okay. It's okay. Yeah, And this is our final answer. So it is to keep him once for divinity. I just want to have a K to K toms to get territorial. Thanks. And here is X two cars, two cakes.

University of Illinois at Urbana-Champaign