Lösungen/Solutions/I1S2AnUe/Ex4

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A=Anhang/Annexe/Appendice

Probl/Ex 1      W

Integrate[Sin[x]^2, {x, 0, Pi}]

Probl/Ex 2      W

Integrate[x Log[x], {x, 1, E}]

Probl/Ex 3      W

Integrate[x^2 Log[x], {x, 1, E}]

Probl/Ex 4      W

Integrate[x^2 Sin[x], {x, 0, Pi}]

Probl/Ex 5      W

Integrate[2 x ln[x^2], x]

Integrate[4 x ln[x^2], {x, a, b}]

Partielle Integration / Intégration partielle

Integrate[x E^(x^2), x]

Integrate[x E^(x^2), {x, y, b}]

Substitution!

Probl/Ex 6      W

D[(x^5 - 6  x^4 + 2  x^3 + 11  x^2 - x + 1)^5, x]

Integrate[(x^5 - 6  x^4 + 2  x^3 + 11  x^2 - x + 1)^4 (5  x^4 - 
            24  x^3 + 6  x^2 + 22  x - 1), x]

1/5  (x^5 - 6  x^4 + 2  x^3 + 11  x^2 - x + 1)^5  // 
      Expand

Probl/Ex 7      W

a

Integrate[1/x^2, {x, 1, Infinity}]

b

Integrate[1/x, {x, 1, Infinity}]

Limit[ln[x], {x -> Infinity}]

c

Integrate[1/x^3, {x, 1, Infinity}]

Probl/Ex 8      W

Integrate[E^(x^2) x^3, {x, 0, 1}]

Probl/Ex 9      W

Integrate[Log[x] Sinh[x], {x, 1, 2}] // N