Optimal. Leaf size=20 \[ \frac {2 \left (x^6-x^2\right )^{3/4}}{3 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1590} \begin {gather*} \frac {2 \left (x^6-x^2\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1590
Rubi steps
\begin {align*} \int \frac {1+x^4}{x^2 \sqrt [4]{-x^2+x^6}} \, dx &=\frac {2 \left (-x^2+x^6\right )^{3/4}}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \left (x^2 \left (x^4-1\right )\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.25, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \left (x^6-x^2\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 16, normalized size = 0.80 \begin {gather*} \frac {2 \, {\left (x^{6} - x^{2}\right )}^{\frac {3}{4}}}{3 \, x^{3}} \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 {x^{4} + 1}{{\left (x^{6} - x^{2}\right )}^{\frac {1}{4}} x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 1.40 \begin {gather*} \frac {2 \left (-1+x \right ) \left (1+x \right ) \left (x^{2}+1\right )}{3 x \left (x^{6}-x^{2}\right )^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{4} + 1}{{\left (x^{6} - x^{2}\right )}^{\frac {1}{4}} x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 16, normalized size = 0.80 \begin {gather*} \frac {2\,{\left (x^6-x^2\right )}^{3/4}}{3\,x^3} \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 {x^{4} + 1}{x^{2} \sqrt [4]{x^{2} \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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