erweitern x(2x+1)^{10}dx

Lösung

erweitern

x (2 x + 1)^{10} d x

1024 x^{11} d x + 5120 x^{10} d x + 11520 x^{9} d x + 15360 x^{8} d x + 13440 x^{7} d x + 8064 x^{6} d x + 3360 x^{5} d x + 960 x^{4} d x + 180 x^{3} d x + 20 x^{2} d x + x d x

Schritte zur Lösung

x (2 x + 1)^{10} d x

(2 x + 1)^{10} = 1024 x^{10} + 5120 x^{9} + 11520 x^{8} + 15360 x^{7} + 13440 x^{6} + 8064 x^{5} + 3360 x^{4} + 960 x^{3} + 180 x^{2} + 20 x + 1

= x (1024 x^{10} + 5120 x^{9} + 11520 x^{8} + 15360 x^{7} + 13440 x^{6} + 8064 x^{5} + 3360 x^{4} + 960 x^{3} + 180 x^{2} + 20 x + 1) d x

Setze Klammern

= x d x \cdot 1024 x^{10} + x d x \cdot 5120 x^{9} + x d x \cdot 11520 x^{8} + x d x \cdot 15360 x^{7} + x d x \cdot 13440 x^{6} + x d x \cdot 8064 x^{5} + x d x \cdot 3360 x^{4} + x d x \cdot 960 x^{3} + x d x \cdot 180 x^{2} + x d x \cdot 20 x + x d x \cdot 1

= 1024 x^{10} x d x + 5120 x^{9} x d x + 11520 x^{8} x d x + 15360 x^{7} x d x + 13440 x^{6} x d x + 8064 x^{5} x d x + 3360 x^{4} x d x + 960 x^{3} x d x + 180 x^{2} x d x + 20 xx d x + 1 \cdot x d x

Vereinfache

1024 x^{10} x d x + 5120 x^{9} x d x + 11520 x^{8} x d x + 15360 x^{7} x d x + 13440 x^{6} x d x + 8064 x^{5} x d x + 3360 x^{4} x d x + 960 x^{3} x d x + 180 x^{2} x d x + 20 xx d x + 1 \cdot x d x : 1024 x^{11} d x + 5120 x^{10} d x + 11520 x^{9} d x + 15360 x^{8} d x + 13440 x^{7} d x + 8064 x^{6} d x + 3360 x^{5} d x + 960 x^{4} d x + 180 x^{3} d x + 20 x^{2} d x + x d x

= 1024 x^{11} d x + 5120 x^{10} d x + 11520 x^{9} d x + 15360 x^{8} d x + 13440 x^{7} d x + 8064 x^{6} d x + 3360 x^{5} d x + 960 x^{4} d x + 180 x^{3} d x + 20 x^{2} d x + x d x

e x p an d 2 (- 5 y + 2 z = - 18)

e x p an d (t u - v)^{2} ln (w - uv)

e x p an d \frac{( 2 yz + 3 x z - x y ) ^{2}}{x ^{2} y ^{2} z ^{2}}

e x p an d \frac{( 4 - x ^{2} )}{( x ^{2} + 4 ) ^{2}}

e x p an d \frac{2 x ln ( x ) - 3 x}{( ln ( x ) - 1 ) ^{2}}