Optimal. Leaf size=31 \[ -\frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-b \log (F) (c+d x)^2\right )}{2 d} \]
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Rubi [A] time = 0.062995, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {2218} \[ -\frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-b \log (F) (c+d x)^2\right )}{2 d} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{F^{a+b (c+d x)^2}}{(c+d x)^9} \, dx &=-\frac{b^4 F^a \Gamma \left (-4,-b (c+d x)^2 \log (F)\right ) \log ^4(F)}{2 d}\\ \end{align*}
Mathematica [A] time = 0.0067544, size = 31, normalized size = 1. \[ -\frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-b \log (F) (c+d x)^2\right )}{2 d} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.091, size = 152, normalized size = 4.9 \begin{align*} -{\frac{{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{8\,d \left ( dx+c \right ) ^{8}}}-{\frac{b\ln \left ( F \right ){F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{24\,d \left ( dx+c \right ) ^{6}}}-{\frac{{b}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{48\,d \left ( dx+c \right ) ^{4}}}-{\frac{{b}^{3} \left ( \ln \left ( F \right ) \right ) ^{3}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{48\,d \left ( dx+c \right ) ^{2}}}-{\frac{{b}^{4} \left ( \ln \left ( F \right ) \right ) ^{4}{F}^{a}{\it Ei} \left ( 1,-b \left ( dx+c \right ) ^{2}\ln \left ( F \right ) \right ) }{48\,d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{9}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{9}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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