Integrate : ∫(ex/x)(1 + x log x) dx, for x ∈ [1,e]. – InterviewSolution

1.

Integrate : ∫(ex/x)(1 + x log x) dx, for x ∈ [1,e].

Answer»

∫(e^x/x)(1 + x log x) dx = ∫e^x((1/x) + log x) dx

= ∫e^x(f(x) + f(x).dx

= e^xf(x) = e^x.log x

∴ ∫(e^x/x)(1 + x log x) dx, for x ∈ [1,e] = [e^x log x], for x ∈ [1,e]

= e^e.log e^e = e log

= e^e

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