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