Optimal. Leaf size=65 \[ \frac {f^{a+b x^2} \left (b^4 x^8 \log ^4(f)-4 b^3 x^6 \log ^3(f)+12 b^2 x^4 \log ^2(f)-24 b x^2 \log (f)+24\right )}{2 b^5 \log ^5(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.37, 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} \[ \frac {f^a \text {Gamma}\left (5,-b x^2 \log (f)\right )}{2 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+b x^2} x^9 \, dx &=\frac {f^a \Gamma \left (5,-b x^2 \log (f)\right )}{2 b^5 \log ^5(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 24, normalized size = 0.37 \[ \frac {f^a \Gamma \left (5,-b x^2 \log (f)\right )}{2 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 63, normalized size = 0.97 \[ \frac {{\left (b^{4} x^{8} \log \relax (f)^{4} - 4 \, b^{3} x^{6} \log \relax (f)^{3} + 12 \, b^{2} x^{4} \log \relax (f)^{2} - 24 \, b x^{2} \log \relax (f) + 24\right )} f^{b x^{2} + a}}{2 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 67, normalized size = 1.03 \[ \frac {{\left (b^{4} x^{8} \log \relax (f)^{4} - 4 \, b^{3} x^{6} \log \relax (f)^{3} + 12 \, b^{2} x^{4} \log \relax (f)^{2} - 24 \, b x^{2} \log \relax (f) + 24\right )} e^{\left (b x^{2} \log \relax (f) + a \log \relax (f)\right )}}{2 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 64, normalized size = 0.98 \[ \frac {\left (b^{4} x^{8} \ln \relax (f )^{4}-4 b^{3} x^{6} \ln \relax (f )^{3}+12 b^{2} x^{4} \ln \relax (f )^{2}-24 b \,x^{2} \ln \relax (f )+24\right ) f^{b \,x^{2}+a}}{2 b^{5} \ln \relax (f )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 77, normalized size = 1.18 \[ \frac {{\left (b^{4} f^{a} x^{8} \log \relax (f)^{4} - 4 \, b^{3} f^{a} x^{6} \log \relax (f)^{3} + 12 \, b^{2} f^{a} x^{4} \log \relax (f)^{2} - 24 \, b f^{a} x^{2} \log \relax (f) + 24 \, f^{a}\right )} f^{b x^{2}}}{2 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.54, size = 63, normalized size = 0.97 \[ \frac {f^{b\,x^2+a}\,\left (\frac {b^4\,x^8\,{\ln \relax (f)}^4}{2}-2\,b^3\,x^6\,{\ln \relax (f)}^3+6\,b^2\,x^4\,{\ln \relax (f)}^2-12\,b\,x^2\,\ln \relax (f)+12\right )}{b^5\,{\ln \relax (f)}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 82, normalized size = 1.26 \[ \begin {cases} \frac {f^{a + b x^{2}} \left (b^{4} x^{8} \log {\relax (f )}^{4} - 4 b^{3} x^{6} \log {\relax (f )}^{3} + 12 b^{2} x^{4} \log {\relax (f )}^{2} - 24 b x^{2} \log {\relax (f )} + 24\right )}{2 b^{5} \log {\relax (f )}^{5}} & \text {for}\: 2 b^{5} \log {\relax (f )}^{5} \neq 0 \\\frac {x^{10}}{10} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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