展开 (x^2+3x+5)^8dx

解答

展开

(x^{2} + 3 x + 5)^{8} d x

x^{16} d x + 24 x^{15} d x + 292 x^{14} d x + 2352 x^{13} d x + 13930 x^{12} d x + 64008 x^{11} d x + 235312 x^{10} d x + 704616 x^{9} d x + 1734931 x^{8} d x + 3523080 x^{7} d x + 5882800 x^{6} d x + 8001000 x^{5} d x + 8706250 x^{4} d x + 7350000 x^{3} d x + 4562500 x^{2} d x + 1875000 x d x + 390625 d x

求解步骤

(x^{2} + 3 x + 5)^{8} d x

(x^{2} + 3 x + 5)^{8} = x^{16} + 24 x^{15} + 292 x^{14} + 2352 x^{13} + 13930 x^{12} + 64008 x^{11} + 235312 x^{10} + 704616 x^{9} + 1734931 x^{8} + 3523080 x^{7} + 5882800 x^{6} + 8001000 x^{5} + 8706250 x^{4} + 7350000 x^{3} + 4562500 x^{2} + 1875000 x + 390625

= (x^{16} + 24 x^{15} + 292 x^{14} + 2352 x^{13} + 13930 x^{12} + 64008 x^{11} + 235312 x^{10} + 704616 x^{9} + 1734931 x^{8} + 3523080 x^{7} + 5882800 x^{6} + 8001000 x^{5} + 8706250 x^{4} + 7350000 x^{3} + 4562500 x^{2} + 1875000 x + 390625) d x

打开括号

= d x x^{16} + d x \cdot 24 x^{15} + d x \cdot 292 x^{14} + d x \cdot 2352 x^{13} + d x \cdot 13930 x^{12} + d x \cdot 64008 x^{11} + d x \cdot 235312 x^{10} + d x \cdot 704616 x^{9} + d x \cdot 1734931 x^{8} + d x \cdot 3523080 x^{7} + d x \cdot 5882800 x^{6} + d x \cdot 8001000 x^{5} + d x \cdot 8706250 x^{4} + d x \cdot 7350000 x^{3} + d x \cdot 4562500 x^{2} + d x \cdot 1875000 x + d x \cdot 390625

= x^{16} d x + 24 x^{15} d x + 292 x^{14} d x + 2352 x^{13} d x + 13930 x^{12} d x + 64008 x^{11} d x + 235312 x^{10} d x + 704616 x^{9} d x + 1734931 x^{8} d x + 3523080 x^{7} d x + 5882800 x^{6} d x + 8001000 x^{5} d x + 8706250 x^{4} d x + 7350000 x^{3} d x + 4562500 x^{2} d x + 1875000 x d x + 390625 d x

e x p an d 524 - 4^{2}

e x p an d (e - 2 f)^{3}

e x p an d e^{x} (1 + c e^{x})

e x p an d (- 3, 4, 2) (2 x - 4 y + z - 7 = 0)

e x p an d \frac{5 ( 1639 - 13 )}{49}