Optimal. Leaf size=34 \[ \frac {f^a \Gamma \left (\frac {13}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{13} \left (-\frac {b \log (f)}{x^2}\right )^{13/2}} \]
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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} \[ \frac {f^a \text {Gamma}\left (\frac {13}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{13} \left (-\frac {b \log (f)}{x^2}\right )^{13/2}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^2}}}{x^{14}} \, dx &=\frac {f^a \Gamma \left (\frac {13}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{13} \left (-\frac {b \log (f)}{x^2}\right )^{13/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ \frac {f^a \Gamma \left (\frac {13}{2},-\frac {b \log (f)}{x^2}\right )}{2 x^{13} \left (-\frac {b \log (f)}{x^2}\right )^{13/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 124, normalized size = 3.65 \[ \frac {10395 \, \sqrt {\pi } \sqrt {-b \log \relax (f)} f^{a} x^{11} \operatorname {erf}\left (\frac {\sqrt {-b \log \relax (f)}}{x}\right ) + 2 \, {\left (10395 \, b x^{10} \log \relax (f) - 6930 \, b^{2} x^{8} \log \relax (f)^{2} + 2772 \, b^{3} x^{6} \log \relax (f)^{3} - 792 \, b^{4} x^{4} \log \relax (f)^{4} + 176 \, b^{5} x^{2} \log \relax (f)^{5} - 32 \, b^{6} \log \relax (f)^{6}\right )} f^{\frac {a x^{2} + b}{x^{2}}}}{128 \, b^{7} x^{11} \log \relax (f)^{7}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x^{14}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 168, normalized size = 4.94 \[ -\frac {10395 \sqrt {\pi }\, f^{a} \erf \left (\frac {\sqrt {-b \ln \relax (f )}}{x}\right )}{128 \sqrt {-b \ln \relax (f )}\, b^{6} \ln \relax (f )^{6}}-\frac {f^{a} f^{\frac {b}{x^{2}}}}{2 b \,x^{11} \ln \relax (f )}+\frac {11 f^{a} f^{\frac {b}{x^{2}}}}{4 b^{2} x^{9} \ln \relax (f )^{2}}-\frac {99 f^{a} f^{\frac {b}{x^{2}}}}{8 b^{3} x^{7} \ln \relax (f )^{3}}+\frac {693 f^{a} f^{\frac {b}{x^{2}}}}{16 b^{4} x^{5} \ln \relax (f )^{4}}-\frac {3465 f^{a} f^{\frac {b}{x^{2}}}}{32 b^{5} x^{3} \ln \relax (f )^{5}}+\frac {10395 f^{a} f^{\frac {b}{x^{2}}}}{64 b^{6} x \ln \relax (f )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.22, size = 28, normalized size = 0.82 \[ \frac {f^{a} \Gamma \left (\frac {13}{2}, -\frac {b \log \relax (f)}{x^{2}}\right )}{2 \, x^{13} \left (-\frac {b \log \relax (f)}{x^{2}}\right )^{\frac {13}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.71, size = 159, normalized size = 4.68 \[ -\frac {\frac {f^a\,\left (\frac {10395\,\sqrt {\pi }\,\mathrm {erfi}\left (\frac {b\,\ln \relax (f)}{x\,\sqrt {b\,\ln \relax (f)}}\right )}{128}-\frac {10395\,f^{\frac {b}{x^2}}\,\sqrt {b\,\ln \relax (f)}}{64\,x}\right )}{\sqrt {b\,\ln \relax (f)}}-\frac {693\,b^2\,f^{a+\frac {b}{x^2}}\,{\ln \relax (f)}^2}{16\,x^5}+\frac {99\,b^3\,f^{a+\frac {b}{x^2}}\,{\ln \relax (f)}^3}{8\,x^7}-\frac {11\,b^4\,f^{a+\frac {b}{x^2}}\,{\ln \relax (f)}^4}{4\,x^9}+\frac {b^5\,f^{a+\frac {b}{x^2}}\,{\ln \relax (f)}^5}{2\,x^{11}}+\frac {3465\,b\,f^{a+\frac {b}{x^2}}\,\ln \relax (f)}{32\,x^3}}{b^6\,{\ln \relax (f)}^6} \]
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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