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11 Homework/Mathe II/Homework 1.typ

@@ -1,29 +1,33 @@
-#let assignment_header(course, index) = {
-  set page(
+#set page(
     header: align(right, [
       #set text(size: 9pt)
       #set par(leading: .3em)
       #pad(y: -.5cm, [
-        #course \
-        Hausaufgabe #index \
+        Mathe II \
+        Hausaufgabe 01 \
         Jan Meyer \
         664237
       ])
     ])
   )
-}
-#assignment_header("Mathe II", 1)
+
 
 == Problem 1 _Stammfunktionen_
-a)
-$ integral x^2 exp(x^3) d x = 1/3 exp(x^3) + C $
+a) $ &integral x^2 exp(x^3) d x = 1/3 exp(x^3) + C $
 
 b)
-$ integral ln(x^2)/x^2 d x = -(2 ln(x) + 2)/x + C $
+$ &integral ln(x^2)/x^2 d x = -(2 ln(x) + 2)/x + C $
 
 c)
-$ integral 1/2 (sin(2x) + 1) d x = 1/4 (-cos(2x) + 2x) + C $
+$ &integral 1/2 (sin(2x) + 1) d x = 1/4 (-cos(2x) + 2x) + C $
+
 
 == Problem 2 _Integrale und Stammfuntionen_
 a)
-$ integral (2x^2 - 3x + 4) / x d x = x^2 - 3x + 4 ln abs(x) $
+$ &integral (2x^2 - 3x + 4) / x d x = x^2 - 3x + 4 ln abs(x) + C $
+
+b)
+$ &integral (2 cos(x)) / (1 + sin(x)) d x = 2 ln abs(1 + sin(x)) + C $
+
+c)
+$ &integral exp(2x) sqrt(1 + exp(2x)) d x = 1/3(1 + exp(2x))^(3/2) + C $