ex1

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
+$ 

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 <https://typst.app/docs/reference/model/numbering/>
+#set footnote(numbering: "*")
+
 #set math.equation(numbering: n => {
   let h1 = counter(heading).get().first()
   numbering("(1.1)", h1, n)

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",
+}