Optimal. Leaf size=34 \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{11/2} \Gamma \left (-\frac {11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
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Rubi [A] time = 0.02, antiderivative size = 34, 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 = {2218} \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{11/2} \text {Gamma}\left (-\frac {11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x^{12}} \, dx &=-\frac {f^a \Gamma \left (-\frac {11}{2},-b x^2 \log (f)\right ) \left (-b x^2 \log (f)\right )^{11/2}}{2 x^{11}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{11/2} \Gamma \left (-\frac {11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 109, normalized size = 3.21 \[ -\frac {32 \, \sqrt {\pi } \sqrt {-b \log \relax (f)} b^{5} f^{a} x^{11} \operatorname {erf}\left (\sqrt {-b \log \relax (f)} x\right ) \log \relax (f)^{5} + {\left (32 \, b^{5} x^{10} \log \relax (f)^{5} + 16 \, b^{4} x^{8} \log \relax (f)^{4} + 24 \, b^{3} x^{6} \log \relax (f)^{3} + 60 \, b^{2} x^{4} \log \relax (f)^{2} + 210 \, b x^{2} \log \relax (f) + 945\right )} f^{b x^{2} + a}}{10395 \, x^{11}} \]
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 \[ \int \frac {f^{b x^{2} + a}}{x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 155, normalized size = 4.56 \[ \frac {32 \sqrt {\pi }\, b^{6} f^{a} \erf \left (\sqrt {-b \ln \relax (f )}\, x \right ) \ln \relax (f )^{6}}{10395 \sqrt {-b \ln \relax (f )}}-\frac {32 b^{5} f^{a} f^{b \,x^{2}} \ln \relax (f )^{5}}{10395 x}-\frac {16 b^{4} f^{a} f^{b \,x^{2}} \ln \relax (f )^{4}}{10395 x^{3}}-\frac {8 b^{3} f^{a} f^{b \,x^{2}} \ln \relax (f )^{3}}{3465 x^{5}}-\frac {4 b^{2} f^{a} f^{b \,x^{2}} \ln \relax (f )^{2}}{693 x^{7}}-\frac {2 b \,f^{a} f^{b \,x^{2}} \ln \relax (f )}{99 x^{9}}-\frac {f^{a} f^{b \,x^{2}}}{11 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 28, normalized size = 0.82 \[ -\frac {\left (-b x^{2} \log \relax (f)\right )^{\frac {11}{2}} f^{a} \Gamma \left (-\frac {11}{2}, -b x^{2} \log \relax (f)\right )}{2 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.63, size = 175, normalized size = 5.15 \[ \frac {32\,f^a\,\sqrt {\pi }\,{\left (-b\,x^2\,\ln \relax (f)\right )}^{11/2}}{10395\,x^{11}}-\frac {f^a\,f^{b\,x^2}}{11\,x^{11}}-\frac {32\,f^a\,\sqrt {\pi }\,\mathrm {erfc}\left (\sqrt {-b\,x^2\,\ln \relax (f)}\right )\,{\left (-b\,x^2\,\ln \relax (f)\right )}^{11/2}}{10395\,x^{11}}-\frac {4\,b^2\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^2}{693\,x^7}-\frac {8\,b^3\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^3}{3465\,x^5}-\frac {16\,b^4\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^4}{10395\,x^3}-\frac {32\,b^5\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^5}{10395\,x}-\frac {2\,b\,f^a\,f^{b\,x^2}\,\ln \relax (f)}{99\,x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{a + b x^{2}}}{x^{12}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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