Optimal. Leaf size=49 \[ -\frac{F^a \left (-b \log (F) (c+d x)^2\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b \log (F) (c+d x)^2\right )}{2 d (c+d x)^{11}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0619664, 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} \[ -\frac{F^a \left (-b \log (F) (c+d x)^2\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b \log (F) (c+d x)^2\right )}{2 d (c+d x)^{11}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{12}} \, dx &=-\frac{F^a \Gamma \left (-\frac{11}{2},-b (c+d x)^2 \log (F)\right ) \left (-b (c+d x)^2 \log (F)\right )^{11/2}}{2 d (c+d x)^{11}}\\ \end{align*}
Mathematica [A] time = 0.0299479, size = 49, normalized size = 1. \[ -\frac{F^a \left (-b \log (F) (c+d x)^2\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b \log (F) (c+d x)^2\right )}{2 d (c+d x)^{11}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.182, size = 228, normalized size = 4.7 \begin{align*} -{\frac{{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{11\,d \left ( dx+c \right ) ^{11}}}-{\frac{2\,b\ln \left ( F \right ){F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{99\,d \left ( dx+c \right ) ^{9}}}-{\frac{4\,{b}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{693\,d \left ( dx+c \right ) ^{7}}}-{\frac{8\,{b}^{3} \left ( \ln \left ( F \right ) \right ) ^{3}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{3465\,d \left ( dx+c \right ) ^{5}}}-{\frac{16\,{b}^{4} \left ( \ln \left ( F \right ) \right ) ^{4}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{10395\,d \left ( dx+c \right ) ^{3}}}-{\frac{32\,{b}^{5} \left ( \ln \left ( F \right ) \right ) ^{5}{F}^{b \left ( dx+c \right ) ^{2}}{F}^{a}}{10395\, \left ( dx+c \right ) d}}+{\frac{32\,{b}^{6} \left ( \ln \left ( F \right ) \right ) ^{6}\sqrt{\pi }{F}^{a}}{10395\,d}{\it Erf} \left ( \sqrt{-b\ln \left ( F \right ) } \left ( dx+c \right ) \right ){\frac{1}{\sqrt{-b\ln \left ( F \right ) }}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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 )}^{12}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 2.05855, size = 1729, normalized size = 35.29 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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 )}^{12}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]