有关定积分的问题,求详解1和3,

需要稍作变换：
∫dx/(11 + 5x)^2
=1/5 * ∫ (5*dx)/(11 + 5x)^2
=1/5 * ∫d(11+5x) /(11 + 5x)^2
=-1/5 *(11+5x)^(-1)|x = -2 → 1
=-1/5 * [1/16 - 1]
=3/16
3. ∫1/(1+e^x) * dx
=∫[(1+e^x) - e^x]/(1 + e^x) * dx
=∫ [1 - e^x/(1+e^x)] * dx
=∫dx - ∫e^x * dx/(1 + e^x)
=∫dx - ∫d(1+ e^x)/(1+e^x)
=x - ln(1 + e^x) |x = 0 →1
=(1 - 0) - [ln(1 + e) - ln(1 + 1)]
= 1 - ln(1 + e) + ln2