Optimal. Leaf size=21 \[ -\frac {\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ -\frac {\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\sqrt {a+c x^4}}{x^7} \, dx &=-\frac {\left (a+c x^4\right )^{3/2}}{6 a x^6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ -\frac {\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 17, normalized size = 0.81 \[ -\frac {{\left (c x^{4} + a\right )}^{\frac {3}{2}}}{6 \, a x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 63, normalized size = 3.00 \[ \frac {3 \, {\left (\sqrt {c} x^{2} - \sqrt {c x^{4} + a}\right )}^{4} c^{\frac {3}{2}} + a^{2} c^{\frac {3}{2}}}{3 \, {\left ({\left (\sqrt {c} x^{2} - \sqrt {c x^{4} + a}\right )}^{2} - a\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ -\frac {\left (c \,x^{4}+a \right )^{\frac {3}{2}}}{6 a \,x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 17, normalized size = 0.81 \[ -\frac {{\left (c x^{4} + a\right )}^{\frac {3}{2}}}{6 \, a x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.22, size = 17, normalized size = 0.81 \[ -\frac {{\left (c\,x^4+a\right )}^{3/2}}{6\,a\,x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.63, size = 42, normalized size = 2.00 \[ - \frac {\sqrt {c} \sqrt {\frac {a}{c x^{4}} + 1}}{6 x^{4}} - \frac {c^{\frac {3}{2}} \sqrt {\frac {a}{c x^{4}} + 1}}{6 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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