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115 days ago by akira093

(1/(x^2-1)).partial_fraction() #部分分数分解 
        
1/2/(x - 1) - 1/2/(x + 1)
1/2/(x - 1) - 1/2/(x + 1)
(x^2-2).find_root(1,2,x) 
        
1.4142135623731364
1.4142135623731364
(x^3+2*x+1).roots(x) #3次方程式も解ける･ω･ 
        
[(-1/2*(I*sqrt(3) + 1)*(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) -
1/3*(I*sqrt(3) - 1)/(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3), 1),
(-1/2*(-I*sqrt(3) + 1)*(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) -
1/3*(-I*sqrt(3) - 1)/(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3), 1),
((1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) - 2/3/(1/18*sqrt(3)*sqrt(59) -
1/2)^(1/3), 1)]
[(-1/2*(I*sqrt(3) + 1)*(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) - 1/3*(I*sqrt(3) - 1)/(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3), 1), (-1/2*(-I*sqrt(3) + 1)*(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) - 1/3*(-I*sqrt(3) - 1)/(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3), 1), ((1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3) - 2/3/(1/18*sqrt(3)*sqrt(59) - 1/2)^(1/3), 1)]
integral(x*cos(x^2), x) # 
        
1/2*sin(x^2)
1/2*sin(x^2)
y = var("y") diff(x*y + sin(x^2) + e^(-x), x) 
        
2*x*cos(x^2) + y - e^(-x)
2*x*cos(x^2) + y - e^(-x)