integral from 5 to 8 of 6/(sqrt(x-5))

解答

\int_{5}^{8} \frac{6}{x - 5} d x

123

十进制

20.78460 \dots

求解步骤

\int_{5}^{8} \frac{6}{x - 5} d x

提出常数:

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

= 6 \cdot \int_{5}^{8} \frac{1}{x - 5} d x

使用换元积分法

= 6 \cdot \int_{0}^{3} 2 d u

常数积分:

\int a d x = a x

= 6 [2 u]_{0}^{3}

带入上下限计算后得:

23

= 6 \cdot 23

化简

= 123

t^{2} y^{^{'}} + y^{2} = t y, y (1) = - \frac{1}{2}

\frac{\partial}{\partial x} (ln (x - y^{2}))

\frac{d y}{d x} = \frac{4 sec ( y )}{( x - 6 ) ^{2}}

\frac{\partial}{\partial x} (x^{2} + x e^{2 y} - y)

\frac{d x}{d y} = 4 (x^{2} + 1)