erweitern 2(2x+8)^7dx

Lösung

erweitern

2 (2 x + 8)^{7} d x

256 x^{7} d x + 7168 x^{6} d x + 86016 x^{5} d x + 573440 x^{4} d x + 2293760 x^{3} d x + 5505024 x^{2} d x + 7340032 x d x + 4194304 d x

Schritte zur Lösung

2 (2 x + 8)^{7} d x

(2 x + 8)^{7} = 128 x^{7} + 3584 x^{6} + 43008 x^{5} + 286720 x^{4} + 1146880 x^{3} + 2752512 x^{2} + 3670016 x + 2097152

= 2 (128 x^{7} + 3584 x^{6} + 43008 x^{5} + 286720 x^{4} + 1146880 x^{3} + 2752512 x^{2} + 3670016 x + 2097152) d x

Setze Klammern

= 2 d x \cdot 128 x^{7} + 2 d x \cdot 3584 x^{6} + 2 d x \cdot 43008 x^{5} + 2 d x \cdot 286720 x^{4} + 2 d x \cdot 1146880 x^{3} + 2 d x \cdot 2752512 x^{2} + 2 d x \cdot 3670016 x + 2 d x \cdot 2097152

= 2 \cdot 128 x^{7} d x + 2 \cdot 3584 x^{6} d x + 2 \cdot 43008 x^{5} d x + 2 \cdot 286720 x^{4} d x + 2 \cdot 1146880 x^{3} d x + 2 \cdot 2752512 x^{2} d x + 2 \cdot 3670016 x d x + 2 \cdot 2097152 d x

Vereinfache

2 \cdot 128 x^{7} d x + 2 \cdot 3584 x^{6} d x + 2 \cdot 43008 x^{5} d x + 2 \cdot 286720 x^{4} d x + 2 \cdot 1146880 x^{3} d x + 2 \cdot 2752512 x^{2} d x + 2 \cdot 3670016 x d x + 2 \cdot 2097152 d x : 256 x^{7} d x + 7168 x^{6} d x + 86016 x^{5} d x + 573440 x^{4} d x + 2293760 x^{3} d x + 5505024 x^{2} d x + 7340032 x d x + 4194304 d x

= 256 x^{7} d x + 7168 x^{6} d x + 86016 x^{5} d x + 573440 x^{4} d x + 2293760 x^{3} d x + 5505024 x^{2} d x + 7340032 x d x + 4194304 d x

e x p an d \frac{1}{( 2 k + 1 ) ( 2 k + 3 )}

e x p an d 3 c - 7

e x p an d \frac{9}{( s + 2 ) ( s + 4 )}

e x p an d (a + e b + e^{2} c)^{3}

e x p an d (ln (x) - 15)^{2}