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Integrate (xsinx - cosx)/x^2 with Intro Calc Techniques
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[QUOTE="The Head, post: 6401780, member: 321011"] [B]Homework Statement:[/B] Evaluate ∫((xsin(x) - cos(x))/x^2. Hint: Use Integration by Parts for sin(x)/x Problem also attached if that's clearer [B]Relevant Equations:[/B] IBP: ∫u dv = uv- ∫v du I'm pretty confused here because after getting stuck on this problem, I tossed it into an integral calculator and it said the answer was 2 Si(x) + cos(x)/x + C. In intro calc we definitely haven't learned the Si(x) function or even gotten to any of the Taylor polynomial stuff yet. I tried IBP for sin(x)/x and got -cos(x)/x - ∫cos(x)/x^2 dx. At first this looked promising, since that is my second term. So I had in total now: -cos(x)/x - 2∫cos(x)/x^2 dx. To do the integral portion, I integrated again (by parts) to find -2∫cos(x)/x^2 dx= 2*cos(x)/x +2∫sin(x)/x dx. Putting it all together, the original integral = -cos(x)/x + 2*cos(x)/x +2∫sin(x)/x dx= cos(x)/x +2∫sin(x)/x dx. I seem to be getting into a loop, where the integral of cos(x)/x^2 is related to the integral of the sin(x)/x, but can't seem to simplify the terms. Help on how to proceed? [/QUOTE]
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Integrate (xsinx - cosx)/x^2 with Intro Calc Techniques
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