Übung: Das Erstellen einfacher Stammfunktionen (2) - MatheNexus

(1)
(2)
(3)
(4)
(5)
(6)
(7)
f1( x)
4x 3
:= − 2x + 1
f2( x)
−3x 5
x 2
:= + − 7x
f3( x)
:=
f4( x)
a x 7
⋅ 4a x 2
= + ⋅ − 2( a + 1)
⋅ x − a
f5( x)
2a x 3
⋅ b x 2
= − ⋅ − 3a ⋅ x − a ⋅ b
f6( x)
4x n
= +
1 ⋅n 1
f7( x)
x2
8 − 3
⋅
7 n
1
⋅ xn − 2 2
− ⋅ x3n
9 +
=
+
(8) f8( x)
= 2 a
Übung: Das Erstellen einfacher Stammfunktionen (2)
Aufgaben: Finde eine Stammfunktion!
1
3 x4 3
4 x2
1
+
7 x −
n 1
2x +
⋅ x n2+ n−3
9 a 2 2n 2
⋅ x +
− ⋅
MK 17.2.2005 Stammfunktion_Ueb2.mcd

Lösungen:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
f1( x)
4x 3
= − 2x + 1
f2( x)
−3x 5
x 2
= + − 7x
1
f3( x)
3 x4 3
4 x2
1
+
7 x −
=
f4( x)
a x 7
⋅ 4a x 2
= + ⋅ − 2( a + 1)
⋅ x − a
f5( x)
2a x 3
⋅ b x 2
= − ⋅ − 3a ⋅ x − a ⋅ b
f6( x)
4x n
= +
1 ⋅n 1
f7( x)
x2
8 − 3
⋅
7 n
1
⋅ xn − 2 2
− ⋅ x3n
9 +
=
+
f8( x)
= 2 a
n 1
2x +
⋅ x n2+ n−3
9 a 2 2n 2
⋅ x +
− ⋅
F1( x)
x 4
x 2
= − + x
x
F2( x)
3
x
3
6
= − −
2
x
F3( x)
5
x
15
3
x
+
4
2
= −
14
F4( x)
F5( x)
F6( x)
=
=
=
a x 8
⋅
8
a x 4
⋅
2
4
n + 1
xn 1
−
+
b x 3
⋅
3
1
F7( x)
16n x2n 3
7 xn
2
= − +
⋅
9 ⋅ ( 3n + 3)
+
2a
F8( x)
n 2
=
⋅
+ n − 2
7 x 2
⋅
2
4 ⋅ a x 3
⋅
+ ( −a − 1)
x
3
2
+ ⋅ − a ⋅ x
3 ⋅ a x 2
⋅
− − a ⋅ b ⋅ x
2
2
n + 2
xn 2
x n2+ n−2
+
−
9a 2
2n + 3
x2n 3
3n 3
x +
+