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1492 days ago by muly22

def f(x): return sin(x^3+2*x)*cos(3*x+5) diff(f(x),x,6) 
        
-(3*x^2 + 2)^6*cos(3*x + 5)*sin(x^3 + 2*x) + 90*(3*x^2 + 2)^4*x*cos(x^3
+ 2*x)*cos(3*x + 5) - 18*(3*x^2 + 2)^5*cos(x^3 + 2*x)*sin(3*x + 5) -
135*(3*x^2 + 2)^4*cos(3*x + 5)*sin(x^3 + 2*x) + 1620*(3*x^2 +
2)^2*x^2*cos(3*x + 5)*sin(x^3 + 2*x) - 1080*(3*x^2 + 2)^3*x*sin(x^3 +
2*x)*sin(3*x + 5) + 4860*(3*x^2 + 2)^2*x*cos(x^3 + 2*x)*cos(3*x + 5) -
3240*x^3*cos(x^3 + 2*x)*cos(3*x + 5) + 120*(3*x^2 + 2)^3*cos(3*x +
5)*sin(x^3 + 2*x) - 540*(3*x^2 + 2)^3*cos(x^3 + 2*x)*sin(3*x + 5) +
9720*(3*x^2 + 2)*x^2*cos(x^3 + 2*x)*sin(3*x + 5) - 2160*(3*x^2 +
2)*x*cos(x^3 + 2*x)*cos(3*x + 5) - 1215*(3*x^2 + 2)^2*cos(3*x +
5)*sin(x^3 + 2*x) + 14580*x^2*cos(3*x + 5)*sin(x^3 + 2*x) + 1080*(3*x^2
+ 2)^2*cos(x^3 + 2*x)*sin(3*x + 5) - 9720*(3*x^2 + 2)*x*sin(x^3 +
2*x)*sin(3*x + 5) + 7290*x*cos(x^3 + 2*x)*cos(3*x + 5) + 3240*(3*x^2 +
2)*cos(3*x + 5)*sin(x^3 + 2*x) - 1458*(3*x^2 + 2)*cos(x^3 + 2*x)*sin(3*x
+ 5) + 6480*x*sin(x^3 + 2*x)*sin(3*x + 5) - 1089*cos(3*x + 5)*sin(x^3 +
2*x) + 3240*cos(x^3 + 2*x)*sin(3*x + 5)
-(3*x^2 + 2)^6*cos(3*x + 5)*sin(x^3 + 2*x) + 90*(3*x^2 + 2)^4*x*cos(x^3 + 2*x)*cos(3*x + 5) - 18*(3*x^2 + 2)^5*cos(x^3 + 2*x)*sin(3*x + 5) - 135*(3*x^2 + 2)^4*cos(3*x + 5)*sin(x^3 + 2*x) + 1620*(3*x^2 + 2)^2*x^2*cos(3*x + 5)*sin(x^3 + 2*x) - 1080*(3*x^2 + 2)^3*x*sin(x^3 + 2*x)*sin(3*x + 5) + 4860*(3*x^2 + 2)^2*x*cos(x^3 + 2*x)*cos(3*x + 5) - 3240*x^3*cos(x^3 + 2*x)*cos(3*x + 5) + 120*(3*x^2 + 2)^3*cos(3*x + 5)*sin(x^3 + 2*x) - 540*(3*x^2 + 2)^3*cos(x^3 + 2*x)*sin(3*x + 5) + 9720*(3*x^2 + 2)*x^2*cos(x^3 + 2*x)*sin(3*x + 5) - 2160*(3*x^2 + 2)*x*cos(x^3 + 2*x)*cos(3*x + 5) - 1215*(3*x^2 + 2)^2*cos(3*x + 5)*sin(x^3 + 2*x) + 14580*x^2*cos(3*x + 5)*sin(x^3 + 2*x) + 1080*(3*x^2 + 2)^2*cos(x^3 + 2*x)*sin(3*x + 5) - 9720*(3*x^2 + 2)*x*sin(x^3 + 2*x)*sin(3*x + 5) + 7290*x*cos(x^3 + 2*x)*cos(3*x + 5) + 3240*(3*x^2 + 2)*cos(3*x + 5)*sin(x^3 + 2*x) - 1458*(3*x^2 + 2)*cos(x^3 + 2*x)*sin(3*x + 5) + 6480*x*sin(x^3 + 2*x)*sin(3*x + 5) - 1089*cos(3*x + 5)*sin(x^3 + 2*x) + 3240*cos(x^3 + 2*x)*sin(3*x + 5)
var('y') def f(x,y): return (x^6+y^3)/((x+y)^2+9) diff(f(x,y),x,y) 
        
-12*(x + y)*x^5/((x + y)^2 + 9)^2 - 6*(x + y)*y^2/((x + y)^2 + 9)^2 +
8*(x^6 + y^3)*(x + y)^2/((x + y)^2 + 9)^3 - 2*(x^6 + y^3)/((x + y)^2 +
9)^2
-12*(x + y)*x^5/((x + y)^2 + 9)^2 - 6*(x + y)*y^2/((x + y)^2 + 9)^2 + 8*(x^6 + y^3)*(x + y)^2/((x + y)^2 + 9)^3 - 2*(x^6 + y^3)/((x + y)^2 + 9)^2
def g(x,y): return diff(f(x,y),x,2,y,3) g(x,y).subs(x=2,y=3) 
        
-12139623/24137569
-12139623/24137569
var('a,b') def k(a,b): return (a+b^3)^10 k(a,b).subs(a=3,b=5) 
        
1180591620717411303424
1180591620717411303424
def f(x): return x^3/1+x^2 integral(f(x),x) 
        
1/4*x^4 + 1/3*x^3
1/4*x^4 + 1/3*x^3
def f(x): return cos(x)^5/(1+sin(x)^2) integral(f(x),x,0.5,1.5) 
        
0.08825886748942158
0.08825886748942158
integral(f(x),x) 
        
1/3*sin(x)^3 + 4*arctan(sin(x)) - 3*sin(x)
1/3*sin(x)^3 + 4*arctan(sin(x)) - 3*sin(x)
def F(x): return 1/3*sin(x)^3 + 4*arctan(sin(x)) - 3*sin(x) F(1.5)-F(0.5) 
        
0.0882588674894214
0.0882588674894214
(pi^2).n(digits=20) 
        
9.8696044010893586188
9.8696044010893586188
a=((x-1)^10*(x+1)^20)/(x^2-1)^5 a.simplify_full() 
        
x^20 + 10*x^19 + 40*x^18 + 70*x^17 - 5*x^16 - 248*x^15 - 400*x^14 -
40*x^13 + 650*x^12 + 780*x^11 - 780*x^9 - 650*x^8 + 40*x^7 + 400*x^6 +
248*x^5 + 5*x^4 - 70*x^3 - 40*x^2 - 10*x - 1
x^20 + 10*x^19 + 40*x^18 + 70*x^17 - 5*x^16 - 248*x^15 - 400*x^14 - 40*x^13 + 650*x^12 + 780*x^11 - 780*x^9 - 650*x^8 + 40*x^7 + 400*x^6 + 248*x^5 + 5*x^4 - 70*x^3 - 40*x^2 - 10*x - 1
def f(x): return x^20 + 10*x^19 + 40*x^18 + 70*x^17 - 5*x^16 - 248*x^15 - 400*x^14 -40*x^13 + 650*x^12 + 780*x^11 - 780*x^9 - 650*x^8 + 40*x^7 + 400*x^6 +248*x^5 + 5*x^4 - 70*x^3 - 40*x^2 - 10*x - 1 factor(f(2)) 
        
3^15
3^15