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Evaluate the following: eeeed∫e6logx-e5logxe4logx-e3logxdx

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Question

Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`

Sum

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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 b^a]

= `int (x^6 - x^5)/(x^4 - x^3) "d"x` .....[∵ e^logx= 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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Evaluation of Definite Integrals by Substitution

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Chapter 7: Integrals - Exercise [Page 163]

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NCERT Exemplar Mathematics Exemplar [English] Class 12

Chapter 7 Integrals
Exercise | Q 4 | Page 163

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Evaluation of Definite Integrals by Substitution

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