3.16.78 \(\int (-x^3+x^4) \, dx\)

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

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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]

-x^4/4 + 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^5}{5}-\frac {x^4}{4} \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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (-x^3+x^4\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[-x^3 + x^4,x]

[Out]

IntegrateAlgebraic[-x^3 + x^4, x]

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fricas [A]  time = 1.04, 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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giac [A]  time = 1.08, 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="giac")

[Out]

1/5*x^5 - 1/4*x^4

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maple [A]  time = 0.00, size = 12, normalized size = 0.80 \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]

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

[Out]

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

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maxima [A]  time = 1.08, 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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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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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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