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(chatquestion)...ulll 47 10:52 PM math.stackexchange.com/c 2 Answers order by votes Since you asked about the indefinite integral, I will introduce a couple of identities and definitions: dt li(æ) = / (1) Int li(x) = Ei(ln æ) (2) -t Ei(=») = - dt. -x Where li(x) is the logarithmic integral, and Ei(x) is the exponential integral. Start by using the substitution you attempted, it is a good one: x = e' + dx = e' dt Hence giving: e7t · et dt dx In x 8t dt dt dt = Substituting u = 8t on the green integral and applying (3), we have: est dt = Ei(u) + cı = Ei du (8 ln æ) + c1

asked Jan 27, 2020 by balaji.thirumalai

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