#let assignment_header(course, index) = {
  set page(
    header: align(right, [
      #set text(size: 9pt)
      #set par(leading: .3em)
      #pad(y: -.5cm, [
        #course \
        Hausaufgabe #index \
        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 $

b)
$ 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 $

== Problem 2 _Integrale und Stammfuntionen_
a)
$ integral (2x^2 - 3x + 4) / x d x = x^2 - 3x + 4 ln abs(x) $