desarrollar f(6x+20)^{22}dx

Solución

desarrollar

f (6 x + 20)^{22} d x

1.31622 E 17 f x^{22} d x + 9.65226 E 18 f x^{21} d x + 3.37829 E 20 f x^{20} d x + 7.50731 E 21 f x^{19} d x + 1.18866 E 23 f x^{18} d x + 1.42639 E 24 f x^{17} d x + 1.34715 E 25 f x^{16} d x + 1.0264 E 26 f x^{15} d x + 6.41498 E 26 f x^{14} d x + 3.32629 E 27 f x^{13} d x + 1.44139 E 28 f x^{12} d x + 1.60154 E 29 f x^{10} d x + 5.24142 E 28 f x^{11} d x + 4.10652 E 29 f x^{9} d x + 8.7997 E 29 f x^{8} d x + 1.56439 E 30 f x^{7} d x + 2.2814 E 30 f x^{6} d x + 2.684 E 30 f x^{5} d x + 2.48519 E 30 f x^{4} d x + 1.74399 E 30 f x^{3} d x + 8.71996 E 29 f x^{2} d x + 2.76824 E 29 f x d x + 4.1943 E 28 fd x

Pasos de solución

f (6 x + 20)^{22} d x

(6 x + 20)^{22} = 1.31622 E 17 x^{22} + 9.65226 E 18 x^{21} + 3.37829 E 20 x^{20} + 7.50731 E 21 x^{19} + 1.18866 E 23 x^{18} + 1.42639 E 24 x^{17} + 1.34715 E 25 x^{16} + 1.0264 E 26 x^{15} + 6.41498 E 26 x^{14} + 3.32629 E 27 x^{13} + \frac{2.04317 E 32 x ^{12} + 2.27019 E 33 x ^{10}}{14175} + 5.24142 E 28 x^{11} + 4.10652 E 29 x^{9} + 8.7997 E 29 x^{8} + 1.56439 E 30 x^{7} + 2.2814 E 30 x^{6} + 2.684 E 30 x^{5} + 2.48519 E 30 x^{4} + 1.74399 E 30 x^{3} + 8.71996 E 29 x^{2} + 2.76824 E 29 x + 4.1943 E 28

= f (1.31622 E 17 x^{22} + 9.65226 E 18 x^{21} + 3.37829 E 20 x^{20} + 7.50731 E 21 x^{19} + 1.18866 E 23 x^{18} + 1.42639 E 24 x^{17} + 1.34715 E 25 x^{16} + 1.0264 E 26 x^{15} + 6.41498 E 26 x^{14} + 3.32629 E 27 x^{13} + 5.24142 E 28 x^{11} + 4.10652 E 29 x^{9} + 8.7997 E 29 x^{8} + 1.56439 E 30 x^{7} + 2.2814 E 30 x^{6} + 2.684 E 30 x^{5} + 2.48519 E 30 x^{4} + 1.74399 E 30 x^{3} + 8.71996 E 29 x^{2} + 2.76824 E 29 x + \frac{2.04317 E 32 x ^{12} + 2.27019 E 33 x ^{10}}{14175} + 4.1943 E 28) d x

Aplicar la siguiente regla de productos notables

= fd x \cdot 1.31622 E 17 x^{22} + fd x \cdot 9.65226 E 18 x^{21} + fd x \cdot 3.37829 E 20 x^{20} + fd x \cdot 7.50731 E 21 x^{19} + fd x \cdot 1.18866 E 23 x^{18} + fd x \cdot 1.42639 E 24 x^{17} + fd x \cdot 1.34715 E 25 x^{16} + fd x \cdot 1.0264 E 26 x^{15} + fd x \cdot 6.41498 E 26 x^{14} + fd x \cdot 3.32629 E 27 x^{13} + fd x \frac{2.04317 E 32 x ^{12} + 2.27019 E 33 x ^{10}}{14175} + fd x \cdot 5.24142 E 28 x^{11} + fd x \cdot 4.10652 E 29 x^{9} + fd x \cdot 8.7997 E 29 x^{8} + fd x \cdot 1.56439 E 30 x^{7} + fd x \cdot 2.2814 E 30 x^{6} + fd x \cdot 2.684 E 30 x^{5} + fd x \cdot 2.48519 E 30 x^{4} + fd x \cdot 1.74399 E 30 x^{3} + fd x \cdot 8.71996 E 29 x^{2} + fd x \cdot 2.76824 E 29 x + fd x \cdot 4.1943 E 28

= 1.31622 E 17 f x^{22} d x + 9.65226 E 18 f x^{21} d x + 3.37829 E 20 f x^{20} d x + 7.50731 E 21 f x^{19} d x + 1.18866 E 23 f x^{18} d x + 1.42639 E 24 f x^{17} d x + 1.34715 E 25 f x^{16} d x + 1.0264 E 26 f x^{15} d x + 6.41498 E 26 f x^{14} d x + 3.32629 E 27 f x^{13} d x + \frac{2.04317 E 32 x ^{12} + 2.27019 E 33 x ^{10}}{14175} fd x + 5.24142 E 28 f x^{11} d x + 4.10652 E 29 f x^{9} d x + 8.7997 E 29 f x^{8} d x + 1.56439 E 30 f x^{7} d x + 2.2814 E 30 f x^{6} d x + 2.684 E 30 f x^{5} d x + 2.48519 E 30 f x^{4} d x + 1.74399 E 30 f x^{3} d x + 8.71996 E 29 f x^{2} d x + 2.76824 E 29 f x d x + 4.1943 E 28 fd x

\frac{2.04317 E 32 x ^{12} + 2.27019 E 33 x ^{10}}{14175} fd x = 1.44139 E 28 f x^{12} d x + 1.60154 E 29 f x^{10} d x

= 1.31622 E 17 f x^{22} d x + 9.65226 E 18 f x^{21} d x + 3.37829 E 20 f x^{20} d x + 7.50731 E 21 f x^{19} d x + 1.18866 E 23 f x^{18} d x + 1.42639 E 24 f x^{17} d x + 1.34715 E 25 f x^{16} d x + 1.0264 E 26 f x^{15} d x + 6.41498 E 26 f x^{14} d x + 3.32629 E 27 f x^{13} d x + 1.44139 E 28 f x^{12} d x + 1.60154 E 29 f x^{10} d x + 5.24142 E 28 f x^{11} d x + 4.10652 E 29 f x^{9} d x + 8.7997 E 29 f x^{8} d x + 1.56439 E 30 f x^{7} d x + 2.2814 E 30 f x^{6} d x + 2.684 E 30 f x^{5} d x + 2.48519 E 30 f x^{4} d x + 1.74399 E 30 f x^{3} d x + 8.71996 E 29 f x^{2} d x + 2.76824 E 29 f x d x + 4.1943 E 28 fd x

e x p an d 2 (e^{x} cos (x)) (e^{x} cos (x) - e^{x} sin (x))

e x p an d \frac{1}{( x - 4 ) ( x ^{2} + 1 )}

e x p an d (z^{2} + cos (z)) (2 z - sin (z))

e x p an d \frac{7 x}{( x + 6 ) ^{2}}

s im pl i f y 2 (1 + \frac{2 k}{n})