Optimal. Leaf size=21 \[ -\frac {\left (a+b x^2\right )^{11/2}}{11 a x^{11}} \]
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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} \[ -\frac {\left (a+b x^2\right )^{11/2}}{11 a x^{11}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^{9/2}}{x^{12}} \, dx &=-\frac {\left (a+b x^2\right )^{11/2}}{11 a x^{11}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ -\frac {\left (a+b x^2\right )^{11/2}}{11 a x^{11}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.98, size = 68, normalized size = 3.24 \[ -\frac {{\left (b^{5} x^{10} + 5 \, a b^{4} x^{8} + 10 \, a^{2} b^{3} x^{6} + 10 \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x^{2} + a^{5}\right )} \sqrt {b x^{2} + a}}{11 \, a x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.06, size = 167, normalized size = 7.95 \[ \frac {2 \, {\left (11 \, {\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{20} b^{\frac {11}{2}} + 165 \, {\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{16} a^{2} b^{\frac {11}{2}} + 462 \, {\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{12} a^{4} b^{\frac {11}{2}} + 330 \, {\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{8} a^{6} b^{\frac {11}{2}} + 55 \, {\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{4} a^{8} b^{\frac {11}{2}} + a^{10} b^{\frac {11}{2}}\right )}}{11 \, {\left ({\left (\sqrt {b} x - \sqrt {b x^{2} + a}\right )}^{2} - a\right )}^{11}} \]
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 \[ -\frac {\left (b \,x^{2}+a \right )^{\frac {11}{2}}}{11 a \,x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.50, size = 17, normalized size = 0.81 \[ -\frac {{\left (b x^{2} + a\right )}^{\frac {11}{2}}}{11 \, a x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.28, size = 111, normalized size = 5.29 \[ -\frac {a^4\,\sqrt {b\,x^2+a}}{11\,x^{11}}-\frac {5\,b^4\,\sqrt {b\,x^2+a}}{11\,x^3}-\frac {10\,a\,b^3\,\sqrt {b\,x^2+a}}{11\,x^5}-\frac {5\,a^3\,b\,\sqrt {b\,x^2+a}}{11\,x^9}-\frac {b^5\,\sqrt {b\,x^2+a}}{11\,a\,x}-\frac {10\,a^2\,b^2\,\sqrt {b\,x^2+a}}{11\,x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.45, size = 150, normalized size = 7.14 \[ - \frac {a^{4} \sqrt {b} \sqrt {\frac {a}{b x^{2}} + 1}}{11 x^{10}} - \frac {5 a^{3} b^{\frac {3}{2}} \sqrt {\frac {a}{b x^{2}} + 1}}{11 x^{8}} - \frac {10 a^{2} b^{\frac {5}{2}} \sqrt {\frac {a}{b x^{2}} + 1}}{11 x^{6}} - \frac {10 a b^{\frac {7}{2}} \sqrt {\frac {a}{b x^{2}} + 1}}{11 x^{4}} - \frac {5 b^{\frac {9}{2}} \sqrt {\frac {a}{b x^{2}} + 1}}{11 x^{2}} - \frac {b^{\frac {11}{2}} \sqrt {\frac {a}{b x^{2}} + 1}}{11 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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