展開する x(2x+5)^8dx

解

展開する

x (2 x + 5)^{8} d x

256 x^{9} d x + 5120 x^{8} d x + 44800 x^{7} d x + 224000 x^{6} d x + 700000 x^{5} d x + 1400000 x^{4} d x + 1750000 x^{3} d x + 1250000 x^{2} d x + 390625 x d x

解答ステップ

x (2 x + 5)^{8} d x

(2 x + 5)^{8} = 256 x^{8} + 5120 x^{7} + 44800 x^{6} + 224000 x^{5} + 700000 x^{4} + 1400000 x^{3} + 1750000 x^{2} + 1250000 x + 390625

= x (256 x^{8} + 5120 x^{7} + 44800 x^{6} + 224000 x^{5} + 700000 x^{4} + 1400000 x^{3} + 1750000 x^{2} + 1250000 x + 390625) d x

括弧を分配する

= x d x \cdot 256 x^{8} + x d x \cdot 5120 x^{7} + x d x \cdot 44800 x^{6} + x d x \cdot 224000 x^{5} + x d x \cdot 700000 x^{4} + x d x \cdot 1400000 x^{3} + x d x \cdot 1750000 x^{2} + x d x \cdot 1250000 x + x d x \cdot 390625

= 256 x^{8} x d x + 5120 x^{7} x d x + 44800 x^{6} x d x + 224000 x^{5} x d x + 700000 x^{4} x d x + 1400000 x^{3} x d x + 1750000 x^{2} x d x + 1250000 xx d x + 390625 x d x

簡素化

256 x^{8} x d x + 5120 x^{7} x d x + 44800 x^{6} x d x + 224000 x^{5} x d x + 700000 x^{4} x d x + 1400000 x^{3} x d x + 1750000 x^{2} x d x + 1250000 xx d x + 390625 x d x : 256 x^{9} d x + 5120 x^{8} d x + 44800 x^{7} d x + 224000 x^{6} d x + 700000 x^{5} d x + 1400000 x^{4} d x + 1750000 x^{3} d x + 1250000 x^{2} d x + 390625 x d x

= 256 x^{9} d x + 5120 x^{8} d x + 44800 x^{7} d x + 224000 x^{6} d x + 700000 x^{5} d x + 1400000 x^{4} d x + 1750000 x^{3} d x + 1250000 x^{2} d x + 390625 x d x