展开 (5x+3)^6dx

解答

展开

(5 x + 3)^{6} d x

15625 x^{6} d x + 56250 x^{5} d x + 84375 x^{4} d x + 67500 x^{3} d x + 30375 x^{2} d x + 7290 x d x + 729 d x

求解步骤

(5 x + 3)^{6} d x

(5 x + 3)^{6} = 15625 x^{6} + 56250 x^{5} + 84375 x^{4} + 67500 x^{3} + 30375 x^{2} + 7290 x + 729

= (15625 x^{6} + 56250 x^{5} + 84375 x^{4} + 67500 x^{3} + 30375 x^{2} + 7290 x + 729) d x

打开括号

= d x \cdot 15625 x^{6} + d x \cdot 56250 x^{5} + d x \cdot 84375 x^{4} + d x \cdot 67500 x^{3} + d x \cdot 30375 x^{2} + d x \cdot 7290 x + d x \cdot 729

= 15625 x^{6} d x + 56250 x^{5} d x + 84375 x^{4} d x + 67500 x^{3} d x + 30375 x^{2} d x + 7290 x d x + 729 d x

e x p an d (6 x^{2} - 3 x^{3}) d x

e x p an d \frac{x - 4}{x ( x - 5 )}

s im pl i f y (x + 1) (\frac{x}{x + 1} + 1)

e x p an d \frac{x}{( 1 + 7 x ) ^{2}}

e x p an d (1 + x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3})^{3} \frac{1}{6}