added some usefull integrals

src/cheatsheets/Analysis1.typ

@@ -606,6 +606,13 @@
       $tan(x) = (2t)/(1-t^2)$,
       $cos(x) = (1-t^2) / (1 + t^2)$,
     )
+
+    *Tricks aus der Schule*
+
+    $integral f(a x+b) d x = 1/a F(a x + b) +c \
+    integral (f'(x))/f(x) d x = ln abs(f(x)) \
+    integral f'(x) e^(f(x)) d x = e^(f(x)) +c \
+    $
   ])
 
   #bgBlock(fill: colorIntegral, [
@@ -671,9 +678,21 @@
     $integral 1/(x-a) d x = ln(x - a) + c\
     integral 1/(x-a)^n d x = - 1/(n-1) 1/(x - a)^(n-1) + c quad "für" n >= 2 \
     integral 1/((x - a)^2 + b^2) d x = 1/b arctan((x - a)/b) + c quad "für" n > 0\
-    integral (x - a)/((x-a)^a + b^2) d x  = 1/2 ln((x-a)^2 + b^2) + c
+    integral (x - a)/((x-a)^a + b^2) d x  = 1/2 ln((x-a)^2 + b^2) + c \    
     $
 
+    #grid(
+      columns: (1fr),
+      column-gutter: 2mm,
+      row-gutter: 4mm,
+      $integral 1/x d x = ln abs(x) +c$,
+      $integral 1/x^2 d x = - 1/x + c$,
+      $integral 1/(a + x) d x = ln abs(a + x) + c$,
+      $integral 1/(a + x)^2 d x = - 1/(a + x) + c$,
+      $integral 1/(a - x) d x = - ln abs(a - x) + c$,
+      $integral 1/(a - x)^2 d x = 1/(a - x) + c$
+    )
+
 
   ])