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Question
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
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Solution
Let `I = int(e^(5 log x) - e^(4 log x))/(e^(3 log x) - e^(2 log x))`
`= int (e^(log x^5) - e^(logx^4))/(e^(log x^3) - e^(log x^2)) dx`
`= int (x^5 - x^4)/(x^3 - x^2)`dx
`= int (x^4(x - 1))/(x^2 (x - 1))`dx
`= int x^4/x^2`dx
`= int x^2 dx`
`= x^3/3 + C`
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