flsimplify(subs(subs(f, 2*t/(1+t 2)', sin(x)), ' (1-t 2)/(1+t 2', 'cos(x) expand(f1) ans=1/2/t+1/2*t+1 1+sin x x(1+cos x) (f1) ans=1/4*t2+t+1/2*log(t) 1+si 2,+n1+c 例2求 f=2*(3-sin(x))/((3+cos(x))*(1+t^2)) f1= simplify(subs(subs(f,2*t/(1+t^2)’,sin(x)’),”(1-t^2)/(1+t^2)’,"’cos(x) f1=(3+3*t^2-2*t)/(2+t^2)/(1+t^2) 利用部分分式展开,积分 nt(f1) f2=1og(2+t^2)+3/2*2(1/2)*atan(/2*t*2^(1/2)-log(1+t^2) dx=In(2+t) 2 clgt-In(1+t)+C 例 求f1=simplify(subs(subs(f,'2*t/(1+t^2)','sin(x)'),'(1-t^2)/(1+t^2)','cos(x) ')) f1 = 1/2*(1+t^2+2*t)/t expand(f1) ans = 1/2/t+1/2*t+1 int(f1) ans = 1/4*t^2+t+1/2*log(t) 例 2 求 f='2*(3-sin(x))/((3+cos(x))*(1+t^2))'; f1=simplify(subs(subs(f,'2*t/(1+t^2)','sin(x)'),'(1-t^2)/(1+t^2)','cos(x) ')) f1 = (3+3*t^2-2*t)/(2+t^2)/(1+t^2) 利用部分分式展开，积分 f2=int(f1) f2 =log(2+t^2)+3/2*2^(1/2)*atan(1/2*t*2^(1/2))-log(1+t^2) 例 3 求