Optimal. Leaf size=16 \[ \frac {3 \left (x^4+1\right )^{5/3}}{5 x^5} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {449} \begin {gather*} \frac {3 \left (x^4+1\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 449
Rubi steps
\begin {align*} \int \frac {\left (-3+x^4\right ) \left (1+x^4\right )^{2/3}}{x^6} \, dx &=\frac {3 \left (1+x^4\right )^{5/3}}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {3 \left (x^4+1\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.10, size = 16, normalized size = 1.00 \begin {gather*} \frac {3 \left (x^4+1\right )^{5/3}}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \, {\left (x^{4} + 1\right )}^{\frac {5}{3}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{4} + 1\right )}^{\frac {2}{3}} {\left (x^{4} - 3\right )}}{x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.81 \begin {gather*} \frac {3 \left (x^{4}+1\right )^{\frac {5}{3}}}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \, {\left (x^{4} + 1\right )}^{\frac {5}{3}}}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 27, normalized size = 1.69 \begin {gather*} \frac {3\,{\left (x^4+1\right )}^{2/3}+3\,x^4\,{\left (x^4+1\right )}^{2/3}}{5\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 2.30, size = 73, normalized size = 4.56 \begin {gather*} \frac {\Gamma \left (- \frac {1}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {2}{3}, - \frac {1}{4} \\ \frac {3}{4} \end {matrix}\middle | {x^{4} e^{i \pi }} \right )}}{4 x \Gamma \left (\frac {3}{4}\right )} - \frac {3 \Gamma \left (- \frac {5}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} - \frac {5}{4}, - \frac {2}{3} \\ - \frac {1}{4} \end {matrix}\middle | {x^{4} e^{i \pi }} \right )}}{4 x^{5} \Gamma \left (- \frac {1}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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