3.20.3 \(\int (\frac {1}{x^5}+x+x^5) \, dx\) [1903]

Optimal. Leaf size=22 \[ -\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6} \]

[Out]

-1/4/x^4+1/2*x^2+1/6*x^6

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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^6}{6}-\frac {1}{4 x^4}+\frac {x^2}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[x^(-5) + x + x^5,x]

[Out]

-1/4*1/x^4 + x^2/2 + x^6/6

Rubi steps

\begin {align*} \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx &=-\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} -\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^(-5) + x + x^5,x]

[Out]

-1/4*1/x^4 + x^2/2 + x^6/6

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Maple [A]
time = 0.01, size = 17, normalized size = 0.77

method	result	size
default	\(-\frac {1}{4 x^{4}}+\frac {x^{2}}{2}+\frac {x^{6}}{6}\)	\(17\)
norman	\(\frac {\frac {1}{6} x^{10}+\frac {1}{2} x^{6}-\frac {1}{4}}{x^{4}}\)	\(17\)
risch	\(-\frac {1}{4 x^{4}}+\frac {x^{2}}{2}+\frac {x^{6}}{6}\)	\(17\)
gosper	\(\frac {2 x^{10}+6 x^{6}-3}{12 x^{4}}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^5+x+x^5,x,method=_RETURNVERBOSE)

[Out]

-1/4/x^4+1/2*x^2+1/6*x^6

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Maxima [A]
time = 0.28, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="maxima")

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4

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Fricas [A]
time = 0.80, size = 17, normalized size = 0.77 \begin {gather*} \frac {2 \, x^{10} + 6 \, x^{6} - 3}{12 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="fricas")

[Out]

1/12*(2*x^10 + 6*x^6 - 3)/x^4

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Sympy [A]
time = 0.02, size = 15, normalized size = 0.68 \begin {gather*} \frac {x^{6}}{6} + \frac {x^{2}}{2} - \frac {1}{4 x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**5+x+x**5,x)

[Out]

x**6/6 + x**2/2 - 1/(4*x**4)

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Giac [A]
time = 1.20, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^5+x+x^5,x, algorithm="giac")

[Out]

1/6*x^6 + 1/2*x^2 - 1/4/x^4

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Mupad [B]
time = 0.03, size = 17, normalized size = 0.77 \begin {gather*} \frac {2\,x^{10}+6\,x^6-3}{12\,x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x + 1/x^5 + x^5,x)

[Out]

(6*x^6 + 2*x^10 - 3)/(12*x^4)

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