Optimal. Leaf size=78 \[ -\frac {f^{a+b x^2} \left (-b^5 x^{10} \log ^5(f)+5 b^4 x^8 \log ^4(f)-20 b^3 x^6 \log ^3(f)+60 b^2 x^4 \log ^2(f)-120 b x^2 \log (f)+120\right )}{2 b^6 \log ^6(f)} \]
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Rubi [C] time = 0.03, antiderivative size = 24, normalized size of antiderivative = 0.31, 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} \[ -\frac {f^a \text {Gamma}\left (6,-b x^2 \log (f)\right )}{2 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+b x^2} x^{11} \, dx &=-\frac {f^a \Gamma \left (6,-b x^2 \log (f)\right )}{2 b^6 \log ^6(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 24, normalized size = 0.31 \[ -\frac {f^a \Gamma \left (6,-b x^2 \log (f)\right )}{2 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 75, normalized size = 0.96 \[ \frac {{\left (b^{5} x^{10} \log \relax (f)^{5} - 5 \, b^{4} x^{8} \log \relax (f)^{4} + 20 \, b^{3} x^{6} \log \relax (f)^{3} - 60 \, b^{2} x^{4} \log \relax (f)^{2} + 120 \, b x^{2} \log \relax (f) - 120\right )} f^{b x^{2} + a}}{2 \, b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 79, normalized size = 1.01 \[ \frac {{\left (b^{5} x^{10} \log \relax (f)^{5} - 5 \, b^{4} x^{8} \log \relax (f)^{4} + 20 \, b^{3} x^{6} \log \relax (f)^{3} - 60 \, b^{2} x^{4} \log \relax (f)^{2} + 120 \, b x^{2} \log \relax (f) - 120\right )} e^{\left (b x^{2} \log \relax (f) + a \log \relax (f)\right )}}{2 \, b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 76, normalized size = 0.97 \[ \frac {\left (b^{5} x^{10} \ln \relax (f )^{5}-5 b^{4} x^{8} \ln \relax (f )^{4}+20 b^{3} x^{6} \ln \relax (f )^{3}-60 b^{2} x^{4} \ln \relax (f )^{2}+120 b \,x^{2} \ln \relax (f )-120\right ) f^{b \,x^{2}+a}}{2 b^{6} \ln \relax (f )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 92, normalized size = 1.18 \[ \frac {{\left (b^{5} f^{a} x^{10} \log \relax (f)^{5} - 5 \, b^{4} f^{a} x^{8} \log \relax (f)^{4} + 20 \, b^{3} f^{a} x^{6} \log \relax (f)^{3} - 60 \, b^{2} f^{a} x^{4} \log \relax (f)^{2} + 120 \, b f^{a} x^{2} \log \relax (f) - 120 \, f^{a}\right )} f^{b x^{2}}}{2 \, b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 76, normalized size = 0.97 \[ -\frac {f^{b\,x^2+a}\,\left (-\frac {b^5\,x^{10}\,{\ln \relax (f)}^5}{2}+\frac {5\,b^4\,x^8\,{\ln \relax (f)}^4}{2}-10\,b^3\,x^6\,{\ln \relax (f)}^3+30\,b^2\,x^4\,{\ln \relax (f)}^2-60\,b\,x^2\,\ln \relax (f)+60\right )}{b^6\,{\ln \relax (f)}^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 95, normalized size = 1.22 \[ \begin {cases} \frac {f^{a + b x^{2}} \left (b^{5} x^{10} \log {\relax (f )}^{5} - 5 b^{4} x^{8} \log {\relax (f )}^{4} + 20 b^{3} x^{6} \log {\relax (f )}^{3} - 60 b^{2} x^{4} \log {\relax (f )}^{2} + 120 b x^{2} \log {\relax (f )} - 120\right )}{2 b^{6} \log {\relax (f )}^{6}} & \text {for}\: 2 b^{6} \log {\relax (f )}^{6} \neq 0 \\\frac {x^{12}}{12} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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