Question

这道题怎么算?

求详细过程

Answer 1

Answer 2

设 x = tanθ。则 dx = sec²θ*dθ，θ=arctanx。那么，这个不定积分可以变换为：
=∫sec²θ*dθ/sec³θ
=∫dθ/secθ
=∫cosθ*dθ
=sinθ + C
=tanθ*cosθ + C
=x * 1/secθ + C
= x/√(1+tan²θ) + C
= x/√(1+x²) + C