dt 解 tg f=1/(a2*t^2+b^2)’;int(f) ans =1/b/a*atan(a*t/b) dtg arc tg-tgx+C 例4 s='t-sart((x+2)/(x-2)): x=solve(f) (1+t^2)/(-1+t^2) simplify(diff (x, 't') ans=-8*t/(-1+t^2)^2 g=-8*t2/(x*(t2-1)2) gl=simplify(subs(g, x',2*(t 2+1)/(t 2-1),)) g1=-4*t2/(1+t^2)/(t2-1) ans =-log(t-1)+log(1+t)-2*atan(t) rctgf+C - dx (1+x)√2 (1+x)(1+x)(2-x) f=t2(2-x)/(1+x): x=solve(f), dx=simplify (t2-2)/(1+t^2) dx=-6*t/(1+t2)2 g=(-6/(1+x)2)/(1+t^2)2解 f='1/(a^2*t^2+b^2)'; int(f) ans = 1/b/a*atan(a*t/b) 例 4 s='t-sqrt((x+2)/(x-2))';x=solve(f) x = 2*(1+t^2)/(-1+t^2) simplify(diff(x,'t')) ans = -8*t/(-1+t^2)^2 g='-8*t^2/(x*(t^2-1)^2)'； g1=simplify(subs(g,'x','2*(t^2+1)/(t^2-1)')) g1 = -4*t^2/(1+t^2)/(t^2-1) int(g1) ans = -log(t-1)+log(1+t)-2*atan(t) f='t^2-(2-x)/(1+x)';x=solve(f), dx=simplify x = -(t^2-2)/(1+t^2) dx = -6*t/(1+t^2)^2 g='(-6/(1+x)^2)/(1+t^2)^2';