3.19.92 \(\int (-x^3+x^4) \, dx\) [1892]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^5}{5}-\frac {x^4}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-x^3 + x^4,x]

[Out]

-1/4*x^4 + x^5/5

Rubi steps

\begin {align*} \int \left (-x^3+x^4\right ) \, dx &=-\frac {x^4}{4}+\frac {x^5}{5}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {x^4}{4}+\frac {x^5}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-x^3 + x^4,x]

[Out]

-1/4*x^4 + x^5/5

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Mathics [A]
time = 1.68, size = 10, normalized size = 0.67 \begin {gather*} \frac {x^4 \left (-5+4 x\right )}{20} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[-x^3 + x^4,x]')

[Out]

x ^ 4 (-5 + 4 x) / 20

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Maple [A]
time = 0.01, size = 12, normalized size = 0.80

method	result	size
gosper	\(\frac {x^{4} \left (-5+4 x \right )}{20}\)	\(11\)
default	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
norman	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
risch	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^4-x^3,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.26, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{5} \, x^{5} - \frac {1}{4} \, x^{4} \end {gather*}

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

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Fricas [A]
time = 0.29, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{5} \, x^{5} - \frac {1}{4} \, x^{4} \end {gather*}

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

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Sympy [A]
time = 0.05, size = 8, normalized size = 0.53 \begin {gather*} \frac {x^{5}}{5} - \frac {x^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**4-x**3,x)

[Out]

x**5/5 - x**4/4

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Giac [A]
time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} \frac {x^{5}}{5}-\frac {x^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4-x^3,x)

[Out]

1/5*x^5 - 1/4*x^4

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Mupad [B]
time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} \frac {x^4\,\left (4\,x-5\right )}{20} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^4 - x^3,x)

[Out]

(x^4*(4*x - 5))/20

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