Optimal. Leaf size=49 \[ \frac{F^a \text{Gamma}\left (\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d (c+d x)^{13} \left (-\frac{b \log (F)}{(c+d x)^2}\right )^{13/2}} \]
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Rubi [A] time = 0.0453299, antiderivative size = 49, 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} \[ \frac{F^a \text{Gamma}\left (\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d (c+d x)^{13} \left (-\frac{b \log (F)}{(c+d x)^2}\right )^{13/2}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{14}} \, dx &=\frac{F^a \Gamma \left (\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d (c+d x)^{13} \left (-\frac{b \log (F)}{(c+d x)^2}\right )^{13/2}}\\ \end{align*}
Mathematica [A] time = 0.026041, size = 49, normalized size = 1. \[ \frac{F^a \text{Gamma}\left (\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d (c+d x)^{13} \left (-\frac{b \log (F)}{(c+d x)^2}\right )^{13/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.341, size = 241, normalized size = 4.9 \begin{align*} -{\frac{{F}^{a}}{2\,d \left ( dx+c \right ) ^{11}b\ln \left ( F \right ) }{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}+{\frac{11\,{F}^{a}}{4\, \left ( \ln \left ( F \right ) \right ) ^{2}{b}^{2}d \left ( dx+c \right ) ^{9}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}-{\frac{99\,{F}^{a}}{8\,d{b}^{3} \left ( \ln \left ( F \right ) \right ) ^{3} \left ( dx+c \right ) ^{7}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}+{\frac{693\,{F}^{a}}{16\,d{b}^{4} \left ( \ln \left ( F \right ) \right ) ^{4} \left ( dx+c \right ) ^{5}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}-{\frac{3465\,{F}^{a}}{32\,d \left ( \ln \left ( F \right ) \right ) ^{5}{b}^{5} \left ( dx+c \right ) ^{3}}{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}+{\frac{10395\,{F}^{a}}{64\,d \left ( \ln \left ( F \right ) \right ) ^{6}{b}^{6} \left ( dx+c \right ) }{F}^{{\frac{b}{ \left ( dx+c \right ) ^{2}}}}}-{\frac{10395\,{F}^{a}\sqrt{\pi }}{128\,d \left ( \ln \left ( F \right ) \right ) ^{6}{b}^{6}}{\it Erf} \left ({\frac{1}{dx+c}\sqrt{-b\ln \left ( F \right ) }} \right ){\frac{1}{\sqrt{-b\ln \left ( F \right ) }}}} \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^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{{\left (d x + c\right )}^{14}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.0817, size = 1750, normalized size = 35.71 \begin{align*} \text{result too large to display} \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^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{{\left (d x + c\right )}^{14}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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