计算下式的定积分
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计算下式的定积分
![](http://img.wesiedu.com/upload/5/5d/55d03d9ef1dade122e1e6d75a4bc8df4.jpg)
![](http://img.wesiedu.com/upload/5/5d/55d03d9ef1dade122e1e6d75a4bc8df4.jpg)
![计算下式的定积分](/uploads/image/z/6888026-2-6.jpg?t=%E8%AE%A1%E7%AE%97%E4%B8%8B%E5%BC%8F%E7%9A%84%E5%AE%9A%E7%A7%AF%E5%88%86)
被积函数f(x)=x√(xx+1)/xx (为方便,用xx表示x平方.下同)
∴积分I=∫(√3~√8)[√(xx+1)/2xx ]dxx 换元t=√(xx+1)并换限,(√3~√8)为积分限,下同
I= ∫(2~3)[tt/(tt-1) ]dt
= ∫(2~3)[1+1/2(t-1) -1/2(t+1)]dt (再积分,得到)
=[t+1/2 ln (t-1)-1/2 ln(t+1) ]│(2~3)
后面的计算相信你会作了.通常这类根式函数的积分可换元(化简后,令根式为积分变量)来作.加油!祝你成功!
∴积分I=∫(√3~√8)[√(xx+1)/2xx ]dxx 换元t=√(xx+1)并换限,(√3~√8)为积分限,下同
I= ∫(2~3)[tt/(tt-1) ]dt
= ∫(2~3)[1+1/2(t-1) -1/2(t+1)]dt (再积分,得到)
=[t+1/2 ln (t-1)-1/2 ln(t+1) ]│(2~3)
后面的计算相信你会作了.通常这类根式函数的积分可换元(化简后,令根式为积分变量)来作.加油!祝你成功!