高等数学不定积分?

如图,这个要怎么做?,求下解释过程,谢谢啦
2025-05-07 14:03:53
推荐回答(1个)
回答1:

23. f(x^2-1) = ln[x^2/(x^2-2)] = ln[(x^2-1+1)/(x^2-1-1)]
得 f(x) = ln[(x+1)/(x-1)];
f[φ(x)] = ln{[φ(x)+1]/[φ(x)-1]} = lnx, [φ(x)+1]/[φ(x)-1] = x,
φ(x)+1 = xφ(x) - x, φ(x) = (x+1)/(x-1);
∫φ(x)dx = ∫[(x+1)/(x-1)]dx = ∫[1+2/(x-1)]dx
= x + 2ln|x-1| + C