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  1. sqrt(1-sin(x)^2) := cos(x)
  2. sqrt(1-cos(x)^2) := sin(x)
  3. (1-sin(x)^2)^(-0.5) := 1/cos(x)
  4. #solv_sub(y_,x_,g_) := inverse(subs(solve(subs(y,g=t),t),t=g))
  5. #solv_sub(sin(x)^2=1,x,sin(x))
  6. #inte_sub(y_,x_,g_) := subs(inte(subs(y,x=inverse(g))*d(inverse(g),x),x), x=g)
  7. #inte_sub(y_,x_,g_) := subs(inte(subs(y,x=g)*d(g,x),x), x=inverse(g))
  8. #inte_sub(exp(-x)/sqrt(x),x,sqrt(x))
  9. #inte_sub(sqrt(1-x^2),x,cos(x))
  10. #d(last,x)
  11. #inte(sin(tan(x))*(1+x^2),x)
  12. inverse(e^x)
  13. inverse(x^6)
  14. inverse(sin(x))
  15.