Lainey Goodwin
2022-01-22
fumanchuecf
Beginner2022-01-23Added 21 answers
If you don't like special functions symbols:
Let
Then
Georgia Ingram
Beginner2022-01-24Added 11 answers
I assume that \(\displaystyle{\log{{x}}}\) denotes the natural logarithm.
The antiderivative you are analyzing has no expression in terms of “elementary function”, just like the case of the antiderivative of \(\displaystyle{e}^{{−{x}^{{2}}}}\).
You can transform it in various ways; with the substitution \(\displaystyle{t}=−{\log{{x}}}\), we have \(\displaystyle{x}={e}−{t}\) and \(dx=−e^{−t}dt\), so we obtain
\(\displaystyle\int{\frac{{{e}^{{−{t}}}}}{{{t}}}}{\left.{d}{t}\right.}\)
but this doesn't help much.
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