求∫1/√20[arccosx/(1-x2)3]dx
【正确答案】：令x=cost，则有
原式=∫π/4π/2[t(-sint)/sin3t]dt
=∫π/2π/4tcsc2tdt
=-∫π/2π/4td(cott)
=-(tcott∣π/2π/4-∫π/2π/4cottdt)
=π/4+ln∣sint∣π/2π/4
=ln√2+π/4=(1/2)ln2+π/4
求∫1/√20[arccosx/(1-x2)3]dx
- 2024-11-07 09:12:04
- 高等数学（经管类）(13125)