Optimal. Leaf size=34 \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{9/2} \Gamma \left (-\frac {9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
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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} \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{9/2} \text {Gamma}\left (-\frac {9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x^{10}} \, dx &=-\frac {f^a \Gamma \left (-\frac {9}{2},-b x^2 \log (f)\right ) \left (-b x^2 \log (f)\right )^{9/2}}{2 x^9}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ -\frac {f^a \left (-b x^2 \log (f)\right )^{9/2} \Gamma \left (-\frac {9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 97, normalized size = 2.85 \[ -\frac {16 \, \sqrt {\pi } \sqrt {-b \log \relax (f)} b^{4} f^{a} x^{9} \operatorname {erf}\left (\sqrt {-b \log \relax (f)} x\right ) \log \relax (f)^{4} + {\left (16 \, b^{4} x^{8} \log \relax (f)^{4} + 8 \, b^{3} x^{6} \log \relax (f)^{3} + 12 \, b^{2} x^{4} \log \relax (f)^{2} + 30 \, b x^{2} \log \relax (f) + 105\right )} f^{b x^{2} + a}}{945 \, x^{9}} \]
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 \[ \int \frac {f^{b x^{2} + a}}{x^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 133, normalized size = 3.91 \[ \frac {16 \sqrt {\pi }\, b^{5} f^{a} \erf \left (\sqrt {-b \ln \relax (f )}\, x \right ) \ln \relax (f )^{5}}{945 \sqrt {-b \ln \relax (f )}}-\frac {16 b^{4} f^{a} f^{b \,x^{2}} \ln \relax (f )^{4}}{945 x}-\frac {8 b^{3} f^{a} f^{b \,x^{2}} \ln \relax (f )^{3}}{945 x^{3}}-\frac {4 b^{2} f^{a} f^{b \,x^{2}} \ln \relax (f )^{2}}{315 x^{5}}-\frac {2 b \,f^{a} f^{b \,x^{2}} \ln \relax (f )}{63 x^{7}}-\frac {f^{a} f^{b \,x^{2}}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.26, size = 28, normalized size = 0.82 \[ -\frac {\left (-b x^{2} \log \relax (f)\right )^{\frac {9}{2}} f^{a} \Gamma \left (-\frac {9}{2}, -b x^{2} \log \relax (f)\right )}{2 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.51, size = 153, normalized size = 4.50 \[ \frac {16\,f^a\,\sqrt {\pi }\,\mathrm {erfc}\left (\sqrt {-b\,x^2\,\ln \relax (f)}\right )\,{\left (-b\,x^2\,\ln \relax (f)\right )}^{9/2}}{945\,x^9}-\frac {16\,f^a\,\sqrt {\pi }\,{\left (-b\,x^2\,\ln \relax (f)\right )}^{9/2}}{945\,x^9}-\frac {f^a\,f^{b\,x^2}}{9\,x^9}-\frac {4\,b^2\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^2}{315\,x^5}-\frac {8\,b^3\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^3}{945\,x^3}-\frac {16\,b^4\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^4}{945\,x}-\frac {2\,b\,f^a\,f^{b\,x^2}\,\ln \relax (f)}{63\,x^7} \]
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 \[ \int \frac {f^{a + b x^{2}}}{x^{10}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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