integral from-a to a of 1/((s-x)^2)

解答

\int_{- a}^{a} \frac{1}{( s - x ) ^{2}} d x

\frac{2 a}{( s - a ) ( a + s )}

求解步骤

\int_{- a}^{a} \frac{1}{( s - x ) ^{2}} d x

使用换元积分法

= \int_{s + a}^{s - a} - \frac{1}{u ^{2}} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{s + a}^{s - a} \frac{1}{u ^{2}} d u

使用幂法则

= - [- \frac{1}{u}]_{s + a}^{s - a}

带入上下限计算后得:

- \frac{1}{s - a} + \frac{1}{s + a}

= - (- \frac{1}{s - a} + \frac{1}{s + a})

化简

= \frac{2 a}{( s - a ) ( a + s )}

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

\int \frac{2}{x ^{\frac{2}{3}}} d x

2 y \cdot \frac{d y}{d x} = x (y^{2} + 1)

\frac{d}{d x} (in (x^{2} - 5))

y^{^{'}} = 1 - e^{x - y + 8}