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

Lösung

erweitern

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

x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

Schritte zur Lösung

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

(x^{3} + 2 x + 3)^{2} = x^{6} + 4 x^{4} + 6 x^{3} + 4 x^{2} + 12 x + 9

= x^{3} (x^{6} + 4 x^{4} + 6 x^{3} + 4 x^{2} + 12 x + 9) d x

Setze Klammern

= x^{3} d x x^{6} + x^{3} d x \cdot 4 x^{4} + x^{3} d x \cdot 6 x^{3} + x^{3} d x \cdot 4 x^{2} + x^{3} d x \cdot 12 x + x^{3} d x \cdot 9

= x^{6} x^{3} d x + 4 x^{4} x^{3} d x + 6 x^{3} x^{3} d x + 4 x^{3} x^{2} d x + 12 x^{3} x d x + 9 x^{3} d x

Vereinfache

x^{6} x^{3} d x + 4 x^{4} x^{3} d x + 6 x^{3} x^{3} d x + 4 x^{3} x^{2} d x + 12 x^{3} x d x + 9 x^{3} d x : x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

= x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

e x p an d e^{2 x} (1 + e^{2 x})^{3} d x

e x p an d (- 3) (4 x - 5 y = 3)

e x p an d - 3 ((- 2, 1, 1) - (4, 3, 5))

e x p an d \frac{( 4 + x ) ^{3}}{8}

e x p an d 3 (e^{3 t} + C e^{- t}) + 8 e^{- t}