展开 (1/(2x)-sqrt(1+x))(sqrt(x))dx

解答

展开

(\frac{1}{2 x} - 1 + x) (x) d x

\frac{d x}{2 x} - d x x + x^{2}

求解步骤

(\frac{1}{2 x} - 1 + x) (x) d x

= (x) (\frac{1}{2 x} - 1 + x) d x

使用分配律:

a (b - c) = ab - a c

a = (x) d x, b = \frac{1}{2 x}, c = 1 + x

= (x) d x \frac{1}{2 x} - (x) d x 1 + x

= \frac{1}{2 x} (x) d x - (x) d x 1 + x

化简

\frac{1}{2 x} (x) d x - (x) d x 1 + x : \frac{d x}{2 x} - d x x + x^{2}

= \frac{d x}{2 x} - d x x + x^{2}

e x p an d (1 + tan (A))^{2}

e x p an d (t + e^{t})^{2}

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 3 y + 4))

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

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