Greetings! I'm not sure how to approach this question, it's asking that I rewrite this: ∫(sin(x)-x)/x^3 dx as an infinite series. Any help is appreciated!
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Write sin(x) as a Taylor's series. Then you can subtract x, divide by and integrate term by term.
Ok let me see...
sinx as a Taylor series would be the sum of ((-1)^n/(2n+1)!)*x^(2n+1)
so then would we have (((-1)^n/(2n+1)!)*x^(2n+1)/x^3) - (x/x^3)?
Yes, and surely you can now simplify...
It might make more sense if you write it out as .
Ah! Alright that makes much more sense now. Thank you very much!
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