展开 2pi(x)(x^{1/2}-3)dx

解答

展开

2 π (x) (x^{\frac{1}{2}} - 3) d x

2 π x^{\frac{3}{2}} d x - 6 π x d x

求解步骤

2 π (x) (x^{\frac{1}{2}} - 3) d x

使用分配律:

a (b - c) = ab - a c

a = 2 π (x) d x, b = x^{\frac{1}{2}}, c = 3

= 2 π (x) d x x^{\frac{1}{2}} - 2 π (x) d x \cdot 3

= 2 π (x) x^{\frac{1}{2}} d x - 2 \cdot 3 π (x) d x

化简

2 π (x) x^{\frac{1}{2}} d x - 2 \cdot 3 π (x) d x : 2 π x^{\frac{3}{2}} d x - 6 π x d x

= 2 π x^{\frac{3}{2}} d x - 6 π x d x

s im pl i f y d H (x^{2} + 1)

e x p an d \frac{1}{( 1 + 3 x ) ^{5}}

e x p an d \frac{( x - 6 ) ^{2}}{( 6 - 5 x )}

e x p an d \frac{2 x ^{2} + 4 x + 1}{( x + 1 ) ( x + 2 ) ^{3}}

e x p an d \frac{( e ^{5 x} - e ^{- 5 x} ) ^{2}}{4}