Integrate the following functions w.r.t. x : exx[x(logx)2+2(logx)] - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`

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Solution

Let I = `int e^x/x [x (logx)^2 + 2log x].dx`

= `int e^x [(logx)^2 + (2logx)/x].dx`

Put f(x) = (log x)2

∴ f'(x) = `d/dx (logx)^2`

= `2 (logx).d/dx (logx)`

= `(2logx)/x`

∴ I = `int e^x [f(x) + f'(x)].dx`

= ex . f(x) + c

= ex . (log x)2 + c.

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Chapter 3: Indefinite Integration - Exercise 3.3 [Page 138]

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