高数定积分计算问题,
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高数定积分计算问题,
![](http://img.wesiedu.com/upload/a/fa/afa4e862d5c67b6012b7532b48ea84a7.jpg)
![](http://img.wesiedu.com/upload/a/fa/afa4e862d5c67b6012b7532b48ea84a7.jpg)
![高数定积分计算问题,](/uploads/image/z/14876479-55-9.jpg?t=%E9%AB%98%E6%95%B0%E5%AE%9A%E7%A7%AF%E5%88%86%E8%AE%A1%E7%AE%97%E9%97%AE%E9%A2%98%2C)
∫1/[e^(x+1)+e^(3-x)]dx 分子分母同乘以e^x
=∫e^x/[e^(2x+1)+e^3]dx
=∫1/[e^(2x+1)+e^3]d(e^x)
=1/e∫1/[e^(2x)+e^2]d(e^x)
=1/e*e*arctan(e^x/e) [0-->+∞]
=π/2-arctan(1/e)
=∫e^x/[e^(2x+1)+e^3]dx
=∫1/[e^(2x+1)+e^3]d(e^x)
=1/e∫1/[e^(2x)+e^2]d(e^x)
=1/e*e*arctan(e^x/e) [0-->+∞]
=π/2-arctan(1/e)