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Question
Evaluate the following:
`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`
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Solution
Let I = `int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`
= `int ("e"^(log x^6) - "e"^(log x^5))/("e"^(logx^4) - "e"^(log x^3)) "d"x` .....[∵ a log b – log ba]
= `int (x^6 - x^5)/(x^4 - x^3) "d"x` .....[∵ elogx = x]
= `int (x^3 - x^2)/(x - 1) "d"x`
= `int (x^2(x - 1))/(x - 1) "d"x`
= `int x^2 "d"x`
= `x^3/3 + "C"`
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