Optimal. Leaf size=37 \[ -\frac {2 \sqrt {1+x^5}}{15 x^{15/2}}+\frac {4 \sqrt {1+x^5}}{15 x^{5/2}} \]
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Rubi [A]
time = 0.00, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {277, 270}
\begin {gather*} \frac {4 \sqrt {x^5+1}}{15 x^{5/2}}-\frac {2 \sqrt {x^5+1}}{15 x^{15/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 277
Rubi steps
\begin {align*} \int \frac {1}{x^{17/2} \sqrt {1+x^5}} \, dx &=-\frac {2 \sqrt {1+x^5}}{15 x^{15/2}}-\frac {2}{3} \int \frac {1}{x^{7/2} \sqrt {1+x^5}} \, dx\\ &=-\frac {2 \sqrt {1+x^5}}{15 x^{15/2}}+\frac {4 \sqrt {1+x^5}}{15 x^{5/2}}\\ \end {align*}
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Mathematica [A]
time = 0.91, size = 25, normalized size = 0.68 \begin {gather*} \frac {2 \sqrt {1+x^5} \left (-1+2 x^5\right )}{15 x^{15/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 20, normalized size = 0.54
method | result | size |
meijerg | \(-\frac {2 \left (-2 x^{5}+1\right ) \sqrt {x^{5}+1}}{15 x^{\frac {15}{2}}}\) | \(20\) |
risch | \(\frac {\frac {2}{15} x^{5}-\frac {2}{15}+\frac {4}{15} x^{10}}{x^{\frac {15}{2}} \sqrt {x^{5}+1}}\) | \(23\) |
gosper | \(\frac {2 \left (x +1\right ) \left (x^{4}-x^{3}+x^{2}-x +1\right ) \left (2 x^{5}-1\right )}{15 x^{\frac {15}{2}} \sqrt {x^{5}+1}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 25, normalized size = 0.68 \begin {gather*} \frac {2 \, \sqrt {x^{5} + 1}}{5 \, x^{\frac {5}{2}}} - \frac {2 \, {\left (x^{5} + 1\right )}^{\frac {3}{2}}}{15 \, x^{\frac {15}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 19, normalized size = 0.51 \begin {gather*} \frac {2 \, {\left (2 \, x^{5} - 1\right )} \sqrt {x^{5} + 1}}{15 \, x^{\frac {15}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {1}{x^{17/2}\,\sqrt {x^5+1}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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