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Zadanie

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x=var('x')
solve([(x^6-9)*(x^5+10)*(x^4+18)*(x^3+49)*(x^2+135)*(x+84) == 0], x)
[x == 1/2*I*3^(5/6) + 1/2*3^(1/3), x == 1/2*I*3^(5/6) - 1/2*3^(1/3), x == -3^(1/3), x == -1/2*I*3^(5/6) - 1/2*3^(1/3), x == -1/2*I*3^(5/6) + 1/2*3^(1/3), x == 3^(1/3), x == 1/4*10^(1/5)*(-1)^(1/5)*(sqrt(5) + I*sqrt(2*sqrt(5) + 10) - 1), x == -1/4*10^(1/5)*(-1)^(1/5)*(sqrt(5) - I*sqrt(-2*sqrt(5) + 10) + 1), x == -1/4*10^(1/5)*(-1)^(1/5)*(sqrt(5) + I*sqrt(-2*sqrt(5) + 10) + 1), x == 1/4*10^(1/5)*(-1)^(1/5)*(sqrt(5) - I*sqrt(2*sqrt(5) + 10) - 1), x == 10^(1/5)*(-1)^(1/5), x == I*sqrt(3)*2^(1/4)*(-1)^(1/4), x == -sqrt(3)*2^(1/4)*(-1)^(1/4), x == -I*sqrt(3)*2^(1/4)*(-1)^(1/4), x == sqrt(3)*2^(1/4)*(-1)^(1/4), x == 1/2*I*49^(1/3)*sqrt(3)*(-1)^(1/3) - 1/2*49^(1/3)*(-1)^(1/3), x == -1/2*I*49^(1/3)*sqrt(3)*(-1)^(1/3) - 1/2*49^(1/3)*(-1)^(1/3), x == 49^(1/3)*(-1)^(1/3), x == -3*I*sqrt(15), x == 3*I*sqrt(15), x == -84] 
x=var('x')
solve([(x^3-5)*(x^2+8)*(x-40) == 0], x)
[x == 1/2*I*5^(1/3)*sqrt(3) - 1/2*5^(1/3), x == -1/2*I*5^(1/3)*sqrt(3) - 1/2*5^(1/3), x == 5^(1/3), x == -2*I*sqrt(2), x == 2*I*sqrt(2), x == 40] 
find_root(cos(x) == x, 0, pi)
0.7390851332151607 
f(x) = x*(sin(x))
integrate(f(x), x)
-x*cos(x) + sin(x) 
f(x) = e^(1/x^2)
integrate(f(x), x, -2, 4)
1/2*I*gamma(-1/2, -1/16) + 1/2*I*gamma(-1/2, -1/4) 
f(x) = sqrt((x^2)*sin(x+2))
diff(f(x), x)
1/2*(x^2*cos(x + 2) + 2*x*sin(x + 2))/sqrt(x^2*sin(x + 2)) 
f(x) = (x*e^(cos(x)))^3
diff(f(x), x)
-3*x^3*e^(3*cos(x))*sin(x) + 3*x^2*e^(3*cos(x)) 
f(x,y) = x^2+sin(x*y)-y
diff(f(x,y), y)
x*cos(x*y) - 1 
x=var('x')
u=function('u', x)
de=diff(u, x, 2)-x*diff(u, x)+ u == 0
desolve(de,u,contrib_ode=True)
[u(x) == _K1*e^(1/2*x^2)*hypergeometric_M(1, 1/2, -1/2*x^2) + _K2*e^(1/2*x^2)*hypergeometric_U(1, 1/2, -1/2*x^2)] 
A=matrix([[1,-4,7],[14,6,8],[-4,-1,2]])
A
[ 1 -4 7] [14 6 8] [-4 -1 2] 
B=matrix([[2,3,9],[-1,17,6],[0,5,-7]])
B
[ 2 3 9] [-1 17 6] [ 0 5 -7] 
A*B
[ 6 -30 -64] [ 22 184 106] [ -7 -19 -56] 
det(A)
330 
B^(-1)
[149/364 -33/182 135/364] [ 1/52 1/26 3/52] [ 5/364 5/182 -37/364]