| Input |
|---|
| 1 – 5 x + x^3 |
| Alternate form |
| x (x^2 – 5) + 1 |
| Polynomial discriminant |
| Delta = 473 |
| Derivative |
| d/dx(1 – 5 x + x^3) = 3 x^2 – 5 |
| Indefinite integral |
| integral (1 – 5 x + x^3) dx = x^4/4 – (5 x^2)/2 + x + constant |
| Local maximum |
| max{1 – 5 x + x^3} = 1 + (10 sqrt(5/3))/3 at x = -sqrt(5/3) |
| Local minimum |
| min{1 – 5 x + x^3} = 1 – (10 sqrt(5/3))/3 at x = sqrt(5/3) |
| Definite integral |
| integral_(-((1 + i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 – i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)))^(-((1 – i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 + i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3))) (1 – 5 x + x^3) dx = -((1 – i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) + ((1 + i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) + (5 (1 – i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)) – (5 (1 + i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)) – 1/4 (-((1 + i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 – i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)))^4 + 1/4 (-((1 – i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 + i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)))^4 – 5 (1/2 (-((1 – i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 + i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)))^2 – 1/2 (-((1 + i sqrt(3)) (1/2 (-9 + i sqrt(1419)))^(1/3))/(2 3^(2/3)) – (5 (1 – i sqrt(3)))/(2^(2/3) (3 (-9 + i sqrt(1419)))^(1/3)))^2)~~-8.63442 |