Optimal. Leaf size=21 \[ -\frac {\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
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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} \[ -\frac {\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+c x^4\right )^{3/2}}{x^{11}} \, dx &=-\frac {\left (a+c x^4\right )^{5/2}}{10 a x^{10}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ -\frac {\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.87, size = 35, normalized size = 1.67 \[ -\frac {{\left (c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right )} \sqrt {c x^{4} + a}}{10 \, a x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.23, size = 92, normalized size = 4.38 \[ \frac {5 \, {\left (\sqrt {c} x^{2} - \sqrt {c x^{4} + a}\right )}^{8} c^{\frac {5}{2}} + 10 \, {\left (\sqrt {c} x^{2} - \sqrt {c x^{4} + a}\right )}^{4} a^{2} c^{\frac {5}{2}} + a^{4} c^{\frac {5}{2}}}{5 \, {\left ({\left (\sqrt {c} x^{2} - \sqrt {c x^{4} + a}\right )}^{2} - a\right )}^{5}} \]
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 \[ -\frac {\left (c \,x^{4}+a \right )^{\frac {5}{2}}}{10 a \,x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 17, normalized size = 0.81 \[ -\frac {{\left (c x^{4} + a\right )}^{\frac {5}{2}}}{10 \, a x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.52, size = 17, normalized size = 0.81 \[ -\frac {{\left (c\,x^4+a\right )}^{5/2}}{10\,a\,x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.50, size = 66, normalized size = 3.14 \[ - \frac {a \sqrt {c} \sqrt {\frac {a}{c x^{4}} + 1}}{10 x^{8}} - \frac {c^{\frac {3}{2}} \sqrt {\frac {a}{c x^{4}} + 1}}{5 x^{4}} - \frac {c^{\frac {5}{2}} \sqrt {\frac {a}{c x^{4}} + 1}}{10 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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