Optimal. Leaf size=23 \[ -\frac {4 \left (10 x^3+3\right ) \left (x^4+x\right )^{3/4}}{63 x^6} \]
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Rubi [A] time = 0.07, antiderivative size = 33, normalized size of antiderivative = 1.43, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2038, 2014} \begin {gather*} -\frac {4 \left (x^4+x\right )^{3/4}}{21 x^6}-\frac {40 \left (x^4+x\right )^{3/4}}{63 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rule 2038
Rubi steps
\begin {align*} \int \frac {1+2 x^3}{x^6 \sqrt [4]{x+x^4}} \, dx &=-\frac {4 \left (x+x^4\right )^{3/4}}{21 x^6}+\frac {10}{7} \int \frac {1}{x^3 \sqrt [4]{x+x^4}} \, dx\\ &=-\frac {4 \left (x+x^4\right )^{3/4}}{21 x^6}-\frac {40 \left (x+x^4\right )^{3/4}}{63 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} -\frac {4 \left (10 x^3+3\right ) \left (x^4+x\right )^{3/4}}{63 x^6} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.28, size = 23, normalized size = 1.00 \begin {gather*} -\frac {4 \left (10 x^3+3\right ) \left (x^4+x\right )^{3/4}}{63 x^6} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 19, normalized size = 0.83 \begin {gather*} -\frac {4 \, {\left (x^{4} + x\right )}^{\frac {3}{4}} {\left (10 \, x^{3} + 3\right )}}{63 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.42, size = 19, normalized size = 0.83 \begin {gather*} -\frac {4}{21} \, {\left (\frac {1}{x^{3}} + 1\right )}^{\frac {7}{4}} - \frac {4}{9} \, {\left (\frac {1}{x^{3}} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 1.35 \begin {gather*} -\frac {4 \left (1+x \right ) \left (x^{2}-x +1\right ) \left (10 x^{3}+3\right )}{63 x^{5} \left (x^{4}+x \right )^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.84, size = 58, normalized size = 2.52 \begin {gather*} -\frac {8 \, {\left (x^{4} + x\right )}}{9 \, {\left (x^{2} - x + 1\right )}^{\frac {1}{4}} {\left (x + 1\right )}^{\frac {1}{4}} x^{\frac {13}{4}}} + \frac {4 \, {\left (4 \, x^{7} + x^{4} - 3 \, x\right )}}{63 \, {\left (x^{2} - x + 1\right )}^{\frac {1}{4}} {\left (x + 1\right )}^{\frac {1}{4}} x^{\frac {25}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 27, normalized size = 1.17 \begin {gather*} -\frac {12\,{\left (x^4+x\right )}^{3/4}+40\,x^3\,{\left (x^4+x\right )}^{3/4}}{63\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 x^{3} + 1}{x^{6} \sqrt [4]{x \left (x + 1\right ) \left (x^{2} - x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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