Optimal. Leaf size=34 \[ \frac {f^a \Gamma \left (\frac {11}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{11} \left (-\frac {b \log (f)}{x^2}\right )^{11/2}} \]
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Rubi [A] time = 0.03, 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} \[ \frac {f^a \text {Gamma}\left (\frac {11}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{11} \left (-\frac {b \log (f)}{x^2}\right )^{11/2}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^2}}}{x^{12}} \, dx &=\frac {f^a \Gamma \left (\frac {11}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{11} \left (-\frac {b \log (f)}{x^2}\right )^{11/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ \frac {f^a \Gamma \left (\frac {11}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{11} \left (-\frac {b \log (f)}{x^2}\right )^{11/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 112, normalized size = 3.29 \[ -\frac {945 \, \sqrt {\pi } \sqrt {-b \log \relax (f)} f^{a} x^{9} \operatorname {erf}\left (\frac {\sqrt {-b \log \relax (f)}}{x}\right ) + 2 \, {\left (945 \, b x^{8} \log \relax (f) - 630 \, b^{2} x^{6} \log \relax (f)^{2} + 252 \, b^{3} x^{4} \log \relax (f)^{3} - 72 \, b^{4} x^{2} \log \relax (f)^{4} + 16 \, b^{5} \log \relax (f)^{5}\right )} f^{\frac {a x^{2} + b}{x^{2}}}}{64 \, b^{6} x^{9} \log \relax (f)^{6}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x^{12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 146, normalized size = 4.29 \[ \frac {945 \sqrt {\pi }\, f^{a} \erf \left (\frac {\sqrt {-b \ln \relax (f )}}{x}\right )}{64 \sqrt {-b \ln \relax (f )}\, b^{5} \ln \relax (f )^{5}}-\frac {f^{a} f^{\frac {b}{x^{2}}}}{2 b \,x^{9} \ln \relax (f )}+\frac {9 f^{a} f^{\frac {b}{x^{2}}}}{4 b^{2} x^{7} \ln \relax (f )^{2}}-\frac {63 f^{a} f^{\frac {b}{x^{2}}}}{8 b^{3} x^{5} \ln \relax (f )^{3}}+\frac {315 f^{a} f^{\frac {b}{x^{2}}}}{16 b^{4} x^{3} \ln \relax (f )^{4}}-\frac {945 f^{a} f^{\frac {b}{x^{2}}}}{32 b^{5} x \ln \relax (f )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 28, normalized size = 0.82 \[ \frac {f^{a} \Gamma \left (\frac {11}{2}, -\frac {b \log \relax (f)}{x^{2}}\right )}{2 \, x^{11} \left (-\frac {b \log \relax (f)}{x^{2}}\right )^{\frac {11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.71, size = 142, normalized size = 4.18 \[ \frac {\frac {f^a\,\left (945\,\sqrt {\pi }\,\mathrm {erfi}\left (\frac {b\,\ln \relax (f)}{x\,\sqrt {b\,\ln \relax (f)}}\right )-\frac {1890\,f^{\frac {b}{x^2}}\,\sqrt {b\,\ln \relax (f)}}{x}\right )}{64\,\sqrt {b\,\ln \relax (f)}}-\frac {63\,b^2\,f^a\,f^{\frac {b}{x^2}}\,{\ln \relax (f)}^2}{8\,x^5}+\frac {9\,b^3\,f^a\,f^{\frac {b}{x^2}}\,{\ln \relax (f)}^3}{4\,x^7}-\frac {b^4\,f^a\,f^{\frac {b}{x^2}}\,{\ln \relax (f)}^4}{2\,x^9}+\frac {315\,b\,f^a\,f^{\frac {b}{x^2}}\,\ln \relax (f)}{16\,x^3}}{b^5\,{\ln \relax (f)}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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