Question

求不定积分 ∫ln[x+(1+x^2)^(1/2)]dx/(1+x^2)^(3/2) 求具体步骤

Answer 1

表面上看似复杂，其实一个分部积分法就搞点啦！

Answer 2

x=tant, (1+x^2)^(1/2) = sect, dx = (sect)^2 dt
原式 = ∫ ln(tant + sect) * cost dt = ∫ ln(tant + sect) d(sint)
= sint ln(tant + sect) - ∫ sint * [ ( sect)^2 + sect tant ] / ( tant + sect) dt
= sint ln(tant + sect) - ∫ sint * sect dt
= sint ln(tant + sect) - ∫ tant dt
= sint ln(tant + sect) + ln cost + C
= ......