erweitern 1/(2x(8+5ln(x))^{10)}

Lösung

erweitern

\frac{1}{2 x ( 8 + 5 ln ( x ) ) ^{10}}

\frac{1}{8 ^{10} \cdot 2 x + 13421772800 x ln ( x ) + 37748736000 x ln ^{2} ( x ) + 62914560000 x ln ^{3} ( x ) + 68812800000 x ln ^{4} ( x ) + 51609600000 x ln ^{5} ( x ) + 26880000000 x ln ^{6} ( x ) + 9600000000 x ln ^{7} ( x ) + 2250000000 x ln ^{8} ( x ) + 312500000 x ln ^{9} ( x ) + 19531250 x ln ^{10} ( x )}

Schritte zur Lösung

\frac{1}{2 x ( 8 + 5 ln ( x ) ) ^{10}}

(8 + 5 ln (x))^{10} = 8^{10} + 6710886400 ln (x) + 18874368000 ln^{2} (x) + 31457280000 ln^{3} (x) + 34406400000 ln^{4} (x) + 25804800000 ln^{5} (x) + 13440000000 ln^{6} (x) + 4800000000 ln^{7} (x) + 1125000000 ln^{8} (x) + 156250000 ln^{9} (x) + 9765625 ln^{10} (x)

= \frac{1}{2 x ( 9765625 ln ^{10} ( x ) + 156250000 ln ^{9} ( x ) + 1125000000 ln ^{8} ( x ) + 4800000000 ln ^{7} ( x ) + 13440000000 ln ^{6} ( x ) + 25804800000 ln ^{5} ( x ) + 34406400000 ln ^{4} ( x ) + 31457280000 ln ^{3} ( x ) + 18874368000 ln ^{2} ( x ) + 6710886400 ln ( x ) + 8 ^{10} )}

Multipliziere aus

2 x (8^{10} + 6710886400 ln (x) + 18874368000 ln^{2} (x) + 31457280000 ln^{3} (x) + 34406400000 ln^{4} (x) + 25804800000 ln^{5} (x) + 13440000000 ln^{6} (x) + 4800000000 ln^{7} (x) + 1125000000 ln^{8} (x) + 156250000 ln^{9} (x) + 9765625 ln^{10} (x)) : 8^{10} \cdot 2 x + 13421772800 x ln (x) + 37748736000 x ln^{2} (x) + 62914560000 x ln^{3} (x) + 68812800000 x ln^{4} (x) + 51609600000 x ln^{5} (x) + 26880000000 x ln^{6} (x) + 9600000000 x ln^{7} (x) + 2250000000 x ln^{8} (x) + 312500000 x ln^{9} (x) + 19531250 x ln^{10} (x)

= \frac{1}{8 ^{10} \cdot 2 x + 13421772800 x ln ( x ) + 37748736000 x ln ^{2} ( x ) + 62914560000 x ln ^{3} ( x ) + 68812800000 x ln ^{4} ( x ) + 51609600000 x ln ^{5} ( x ) + 26880000000 x ln ^{6} ( x ) + 9600000000 x ln ^{7} ( x ) + 2250000000 x ln ^{8} ( x ) + 312500000 x ln ^{9} ( x ) + 19531250 x ln ^{10} ( x )}

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

e x p an d Q (- 3, 2) R (1, 2) S (1, - 4) T (- 3, - 4)

e x p an d - 4 (x - 4) (x - 3)

e x p an d \frac{( m - 2 ) ( 2 m - 1 )}{m ^{2} - 5}

e x p an d \frac{2 ( 6 - 29 )}{7}