3.1892 \(\int \left (-x^3+x^4\right ) \, dx\)

Optimal. Leaf size=15 \[ \frac{x^5}{5}-\frac{x^4}{4} \]

[Out]

-x^4/4 + x^5/5

_______________________________________________________________________________________

Rubi [A]  time = 0.00702779, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{x^5}{5}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]  Int[-x^3 + x^4,x]

[Out]

-x^4/4 + x^5/5

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.12936, size = 8, normalized size = 0.53 \[ \frac{x^{5}}{5} - \frac{x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4-x**3,x)

[Out]

x**5/5 - x**4/4

_______________________________________________________________________________________

Mathematica [A]  time = 0.000056317, size = 15, normalized size = 1. \[ \frac{x^5}{5}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[-x^3 + x^4,x]

[Out]

-x^4/4 + x^5/5

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 12, normalized size = 0.8 \[ -{\frac{{x}^{4}}{4}}+{\frac{{x}^{5}}{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4-x^3,x)

[Out]

-1/4*x^4+1/5*x^5

_______________________________________________________________________________________

Maxima [A]  time = 1.32982, size = 15, normalized size = 1. \[ \frac{1}{5} \, x^{5} - \frac{1}{4} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4 - x^3,x, algorithm="maxima")

[Out]

1/5*x^5 - 1/4*x^4

_______________________________________________________________________________________

Fricas [A]  time = 0.174786, size = 1, normalized size = 0.07 \[ \frac{1}{5} x^{5} - \frac{1}{4} x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4 - x^3,x, algorithm="fricas")

[Out]

1/5*x^5 - 1/4*x^4

_______________________________________________________________________________________

Sympy [A]  time = 0.028972, size = 8, normalized size = 0.53 \[ \frac{x^{5}}{5} - \frac{x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4-x**3,x)

[Out]

x**5/5 - x**4/4

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.268904, size = 15, normalized size = 1. \[ \frac{1}{5} \, x^{5} - \frac{1}{4} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4 - x^3,x, algorithm="giac")

[Out]

1/5*x^5 - 1/4*x^4