Optimal. Leaf size=26 \[ \frac {\left (x^4+1\right )^{3/4} \left (-27 x^8+x^4+28\right )}{77 x^{11}} \]
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Rubi [A] time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.27, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {453, 264} \begin {gather*} \frac {4 \left (x^4+1\right )^{7/4}}{11 x^{11}}-\frac {27 \left (x^4+1\right )^{7/4}}{77 x^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rule 453
Rubi steps
\begin {align*} \int \frac {\left (-4+x^4\right ) \left (1+x^4\right )^{3/4}}{x^{12}} \, dx &=\frac {4 \left (1+x^4\right )^{7/4}}{11 x^{11}}+\frac {27}{11} \int \frac {\left (1+x^4\right )^{3/4}}{x^8} \, dx\\ &=\frac {4 \left (1+x^4\right )^{7/4}}{11 x^{11}}-\frac {27 \left (1+x^4\right )^{7/4}}{77 x^7}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.88 \begin {gather*} \frac {\left (28-27 x^4\right ) \left (x^4+1\right )^{7/4}}{77 x^{11}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.17, size = 23, normalized size = 0.88 \begin {gather*} \frac {\left (28-27 x^4\right ) \left (x^4+1\right )^{7/4}}{77 x^{11}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 24, normalized size = 0.92 \begin {gather*} -\frac {{\left (27 \, x^{8} - x^{4} - 28\right )} {\left (x^{4} + 1\right )}^{\frac {3}{4}}}{77 \, x^{11}} \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 {3}{4}} {\left (x^{4} - 4\right )}}{x^{12}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 20, normalized size = 0.77 \begin {gather*} -\frac {\left (27 x^{4}-28\right ) \left (x^{4}+1\right )^{\frac {7}{4}}}{77 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 25, normalized size = 0.96 \begin {gather*} -\frac {5 \, {\left (x^{4} + 1\right )}^{\frac {7}{4}}}{7 \, x^{7}} + \frac {4 \, {\left (x^{4} + 1\right )}^{\frac {11}{4}}}{11 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 38, normalized size = 1.46 \begin {gather*} \frac {28\,{\left (x^4+1\right )}^{3/4}+x^4\,{\left (x^4+1\right )}^{3/4}-27\,x^8\,{\left (x^4+1\right )}^{3/4}}{77\,x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.37, size = 136, normalized size = 5.23 \begin {gather*} \frac {\left (1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {7}{4}\right )}{4 \Gamma \left (- \frac {3}{4}\right )} - \frac {\left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{x^{3} \Gamma \left (- \frac {3}{4}\right )} + \frac {\left (1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {7}{4}\right )}{4 x^{4} \Gamma \left (- \frac {3}{4}\right )} + \frac {3 \left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{4 x^{7} \Gamma \left (- \frac {3}{4}\right )} + \frac {7 \left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{4 x^{11} \Gamma \left (- \frac {3}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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