Optimal. Leaf size=16 \[ \frac {\left (x^4-1\right )^{7/4}}{7 x^7} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {264} \begin {gather*} \frac {\left (x^4-1\right )^{7/4}}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (-1+x^4\right )^{3/4}}{x^8} \, dx &=\frac {\left (-1+x^4\right )^{7/4}}{7 x^7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {\left (x^4-1\right )^{7/4}}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.13, size = 16, normalized size = 1.00 \begin {gather*} \frac {\left (x^4-1\right )^{7/4}}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 12, normalized size = 0.75 \begin {gather*} \frac {{\left (x^{4} - 1\right )}^{\frac {7}{4}}}{7 \, x^{7}} \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}}}{x^{8}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 24, normalized size = 1.50 \begin {gather*} \frac {\left (-1+x \right ) \left (1+x \right ) \left (x^{2}+1\right ) \left (x^{4}-1\right )^{\frac {3}{4}}}{7 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 12, normalized size = 0.75 \begin {gather*} \frac {{\left (x^{4} - 1\right )}^{\frac {7}{4}}}{7 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 25, normalized size = 1.56 \begin {gather*} -\frac {{\left (x^4-1\right )}^{3/4}-x^4\,{\left (x^4-1\right )}^{3/4}}{7\,x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.98, size = 126, normalized size = 7.88 \begin {gather*} \begin {cases} \frac {\left (-1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} e^{- \frac {i \pi }{4}} \Gamma \left (- \frac {7}{4}\right )}{4 \Gamma \left (- \frac {3}{4}\right )} - \frac {\left (-1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} e^{- \frac {i \pi }{4}} \Gamma \left (- \frac {7}{4}\right )}{4 x^{4} \Gamma \left (- \frac {3}{4}\right )} & \text {for}\: \frac {1}{\left |{x^{4}}\right |} > 1 \\- \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 (1 - \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {7}{4}\right )}{4 x^{4} \Gamma \left (- \frac {3}{4}\right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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