diff --git a/build/main.pdf b/build/main.pdf
index a60b94c..41c50e9 100644
Binary files a/build/main.pdf and b/build/main.pdf differ
diff --git a/src/exercise/1.typ b/src/exercise/1.typ
index 5279850..c1c178f 100644
--- a/src/exercise/1.typ
+++ b/src/exercise/1.typ
@@ -148,23 +148,23 @@ $
   Calculate the following integrals using substitution:
 
   #set enum(numbering: "(a)")
-  + $ integral (2x+7)/(x^2+7x+3) d x $
-  + $ integral (cos(ln(x)))/(x) d x $
+  + $ integral (2x+7)/(x^2+7x+3) thin d x $
+  + $ integral (cos(ln(x)))/(x) thin d x $
 ])
 
 #set enum(numbering: "(a)")
 + $
-  A &= integral (2x+7)/(x^2+7x+3) d x \
-  &= integral (a'(x))/(a(x)) d x \
-  &= integral (a'(x))/(a(x)) d x \
-  &= integral 1/(a(x)) dot a'(x) d x; wide d u = a'(x) d x \
+  A &= integral (2x+7)/(x^2+7x+3) thin d x \
+  &= integral (a'(x))/(a(x)) thin d x \
+  &= integral (a'(x))/(a(x)) thin d x \
+  &= integral 1/(a(x)) dot a'(x) thin d x; wide d u = a'(x) thin d x \
   &= integral 1/u d u \
   &= ln(u) = ln(x^2+7x+3) checkmark
 $
 + $
-  A &= integral (cos(ln(x)))/(x) d x \
-  &= integral cos(ln(x)) dot 1/x d x \
-  &= integral cos(u) dot u' d x \
+  A &= integral (cos(ln(x)))/(x) thin d x \
+  &= integral cos(ln(x)) dot 1/x thin d x \
+  &= integral cos(u) dot u' thin d x \
   &= integral cos(u) dot d u \
   &= sin(u) \
   &= sin(ln(x)) \
@@ -180,16 +180,23 @@ $
   Calculate the following integrals using partial integration:
 
   #set enum(numbering: "(a)")
-  + $ integral (x+2) dot e^(2x) d x $
-  + $ integral x^2 dot ln(x) d x $
+  + $ integral (x+2) dot e^(2x) thin d x $
+  + $ integral x^2 dot ln(x) thin d x $
 ])
 
 #set enum(numbering: "(a)")
 + $
-  A &= integral (x+2) dot e^(2x) d x \
-  &= integral u(x) dot v'(x) d x \
-  &= u(x) dot v(x) - integral u'(x) dot v(x) d x \
-  &= (x+2) dot (e^(2x) dot 1/2x) - integral e^(2x) d x \
-  &= (x+2) dot (e^(2x) dot 1/2x) - e^(2x) dot 1/2x \
-  &= x dot (e^(2x) dot 1/2x) + e^(2x) dot 1/2x \
-$
+  u(x) &= x => u'(x) = 1; space v(x) = e^(2x) dot 1/2 x => v'(x) = e^(2x) \
+  A &= integral (x+2) dot e^(2x) thin d x \
+  &= integral x dot e^(2x) thin d x + integral 2 dot e^(2x) thin d x wide \
+  &= integral x dot e^(2x) thin d x + 2 dot integral e^(2x) thin d x \
+  &= integral x dot e^(2x) thin d x + 2 dot 1/2  e^(2x) \
+  &= integral x dot e^(2x) thin d x + e^(2x) \
+  &= integral u(x) dot v'(x) thin d x + e^(2x) \
+  &= [u(x) dot v(x)] - integral u'(x) dot v(x) thin d x + e^(2x) \
+  &= x dot e^(2x) dot 1/2 - integral 1 dot e^(2x) dot 1/2 thin d x + e^(2x) \
+  &= 1/2 x dot e^(2x) - e^(2x) 1/4 + e^(2x) \
+  &= 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
+| $