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a/src/exercise/1.typ b/src/exercise/1.typ index c1c178f..f9f3f50 100644 --- a/src/exercise/1.typ +++ b/src/exercise/1.typ @@ -199,4 +199,25 @@ $ &= e^(2x) dot (1/2 x - 1/4 + 1) \ &= 1/2 e^(2x) dot (x - 1/2 + 2) \ &= 1/2 e^(2x) dot (x + 3/2) checkmark -| $ +$ ++ $ + u(x) &= x^2 => u'(x) = 2x; space + v(x) = ln(x) dot x - x #footnote([für Hochleitung $ln(x)$ siehe @ln-hochleitung]) + => v'(x) = ln(x) \ + A &= integral x^2 dot ln(x) thin d x \ + &= integral u(x) dot v'(x) thin d x \ + &= [u(x) dot v(x)] - integral u'(x) dot v(x) thin d x \ + &= [x^2 dot (ln(x) dot x - x)] - integral 2x dot (ln(x) dot x - x) thin d x \ + &= [x^2 dot (ln(x) dot x - x)] - 2 dot integral x^2 dot (ln(x) - 1) thin d x \ + &=> ??? \ \ + + + u'(x) &= x^2 => u(x) = 3x^3 dot 1/3; space v(x) = ln(x) => v'(x) = 1/x \ + A &= integral x^2 dot ln(x) thin d x \ + &= integral u'(x) dot v(x) thin d x \ + &= u(x) dot v(x) - integral u(x) dot v'(x) thin d x \ + &= 1/3 x^3 dot ln(x) - integral 1/3 x^3 dot 1/x thin d x \ + &= 1/3 x^3 dot ln(x) - integral 1/3 x^2 thin d x \ + &= 1/3 x^3 dot ln(x) - 1/9 x^3 \ + &= 1/3 x^3 (ln(x) - 1/9) checkmark +$ diff --git a/src/main.typ b/src/main.typ index e2200a8..bd61b41 100644 --- a/src/main.typ +++ b/src/main.typ @@ -41,6 +41,15 @@ it } +// count with symbols +// +// > The * character means that symbols should be used to count, in the +// > order of *, †, ‡, §, ¶, and ‖. If there are more than six items, +// > the number is represented using multiple symbols. +// +// See +#set footnote(numbering: "*") + #set math.equation(numbering: n => { let h1 = counter(heading).get().first() numbering("(1.1)", h1, n) diff --git a/src/refs.bib b/src/refs.bib index 40fb7ca..463cafb 100644 --- a/src/refs.bib +++ b/src/refs.bib @@ -11,8 +11,15 @@ } @online{MatheNichtFreaks, + title = "Mathe für Nicht-Freaks: Teleskopsumme und Teleskop", url = " https://de.wikibooks.org/wiki/Mathe_f%C3%BCr_Nicht-Freaks:_Teleskopsumme_und_Teleskopreihe ", urldate = "2024-07-18", } + +@online{ln-hochleitung, + title = "Herleitung der Stammfunktion des natürlichen Logarithmus", + url = "https://matheguru.com/integralrechnung/herleitung-der-stammfunktion-des-naturlichen-logarithmus.html", + urldate = "2024-09-09", +}