erweitern x^2(x^3+5)^8dx

Lösung

erweitern

x^{2} (x^{3} + 5)^{8} d x

x^{26} d x + 40 x^{23} d x + 700 x^{20} d x + 7000 x^{17} d x + 43750 x^{14} d x + 175000 x^{11} d x + 437500 x^{8} d x + 625000 x^{5} d x + 390625 x^{2} d x

Schritte zur Lösung

x^{2} (x^{3} + 5)^{8} d x

(x^{3} + 5)^{8} = x^{24} + 40 x^{21} + 700 x^{18} + 7000 x^{15} + 43750 x^{12} + 175000 x^{9} + 437500 x^{6} + 625000 x^{3} + 390625

= x^{2} (x^{24} + 40 x^{21} + 700 x^{18} + 7000 x^{15} + 43750 x^{12} + 175000 x^{9} + 437500 x^{6} + 625000 x^{3} + 390625) d x

Setze Klammern

= x^{2} d x x^{24} + x^{2} d x \cdot 40 x^{21} + x^{2} d x \cdot 700 x^{18} + x^{2} d x \cdot 7000 x^{15} + x^{2} d x \cdot 43750 x^{12} + x^{2} d x \cdot 175000 x^{9} + x^{2} d x \cdot 437500 x^{6} + x^{2} d x \cdot 625000 x^{3} + x^{2} d x \cdot 390625

= x^{24} x^{2} d x + 40 x^{21} x^{2} d x + 700 x^{18} x^{2} d x + 7000 x^{15} x^{2} d x + 43750 x^{12} x^{2} d x + 175000 x^{9} x^{2} d x + 437500 x^{6} x^{2} d x + 625000 x^{3} x^{2} d x + 390625 x^{2} d x

Vereinfache

x^{24} x^{2} d x + 40 x^{21} x^{2} d x + 700 x^{18} x^{2} d x + 7000 x^{15} x^{2} d x + 43750 x^{12} x^{2} d x + 175000 x^{9} x^{2} d x + 437500 x^{6} x^{2} d x + 625000 x^{3} x^{2} d x + 390625 x^{2} d x : x^{26} d x + 40 x^{23} d x + 700 x^{20} d x + 7000 x^{17} d x + 43750 x^{14} d x + 175000 x^{11} d x + 437500 x^{8} d x + 625000 x^{5} d x + 390625 x^{2} d x

= x^{26} d x + 40 x^{23} d x + 700 x^{20} d x + 7000 x^{17} d x + 43750 x^{14} d x + 175000 x^{11} d x + 437500 x^{8} d x + 625000 x^{5} d x + 390625 x^{2} d x

e x p an d (- 1 - 12) \cdot ((2, 0, 3) + (3, 1, 1))

e x p an d \frac{2 x}{( 1 + x ) ^{2}}

e x p an d (e^{x} - 2 e^{2 x}) (- 6 e^{x} + 1)

e x p an d \frac{b}{( x + b + 1 ) ( x + 1 )}

e x p an d 5 (6 x + 7 + 4 = 29)