Optimal. Leaf size=31 \[ \frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-b (c+d x)^2 \log (F)\right )}{2 d} \]
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Rubi [A] time = 0.06, antiderivative size = 31, normalized size of antiderivative = 1.00, 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} \[ \frac {b^5 F^a \log ^5(F) \text {Gamma}\left (-5,-b \log (F) (c+d x)^2\right )}{2 d} \]
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)^{11}} \, dx &=\frac {b^5 F^a \Gamma \left (-5,-b (c+d x)^2 \log (F)\right ) \log ^5(F)}{2 d}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ \frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-b (c+d x)^2 \log (F)\right )}{2 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.46, size = 596, normalized size = 19.23 \[ \frac {{\left (b^{5} d^{10} x^{10} + 10 \, b^{5} c d^{9} x^{9} + 45 \, b^{5} c^{2} d^{8} x^{8} + 120 \, b^{5} c^{3} d^{7} x^{7} + 210 \, b^{5} c^{4} d^{6} x^{6} + 252 \, b^{5} c^{5} d^{5} x^{5} + 210 \, b^{5} c^{6} d^{4} x^{4} + 120 \, b^{5} c^{7} d^{3} x^{3} + 45 \, b^{5} c^{8} d^{2} x^{2} + 10 \, b^{5} c^{9} d x + b^{5} c^{10}\right )} F^{a} {\rm Ei}\left ({\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \relax (F)\right ) \log \relax (F)^{5} - {\left ({\left (b^{4} d^{8} x^{8} + 8 \, b^{4} c d^{7} x^{7} + 28 \, b^{4} c^{2} d^{6} x^{6} + 56 \, b^{4} c^{3} d^{5} x^{5} + 70 \, b^{4} c^{4} d^{4} x^{4} + 56 \, b^{4} c^{5} d^{3} x^{3} + 28 \, b^{4} c^{6} d^{2} x^{2} + 8 \, b^{4} c^{7} d x + b^{4} c^{8}\right )} \log \relax (F)^{4} + {\left (b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + 15 \, b^{3} c^{2} d^{4} x^{4} + 20 \, b^{3} c^{3} d^{3} x^{3} + 15 \, b^{3} c^{4} d^{2} x^{2} + 6 \, b^{3} c^{5} d x + b^{3} c^{6}\right )} \log \relax (F)^{3} + 2 \, {\left (b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right )} \log \relax (F)^{2} + 6 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \relax (F) + 24\right )} F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{240 \, {\left (d^{11} x^{10} + 10 \, c d^{10} x^{9} + 45 \, c^{2} d^{9} x^{8} + 120 \, c^{3} d^{8} x^{7} + 210 \, c^{4} d^{7} x^{6} + 252 \, c^{5} d^{6} x^{5} + 210 \, c^{6} d^{5} x^{4} + 120 \, c^{7} d^{4} x^{3} + 45 \, c^{8} d^{3} x^{2} + 10 \, c^{9} d^{2} x + c^{10} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.17, size = 185, normalized size = 5.97 \[ -\frac {b^{5} F^{a} \Ei \left (1, -\left (d x +c \right )^{2} b \ln \relax (F )\right ) \ln \relax (F )^{5}}{240 d}-\frac {b^{4} F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )^{4}}{240 \left (d x +c \right )^{2} d}-\frac {b^{3} F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )^{3}}{240 \left (d x +c \right )^{4} d}-\frac {b^{2} F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )^{2}}{120 \left (d x +c \right )^{6} d}-\frac {b \,F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )}{40 \left (d x +c \right )^{8} d}-\frac {F^{a} F^{\left (d x +c \right )^{2} b}}{10 \left (d x +c \right )^{10} d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.91, size = 136, normalized size = 4.39 \[ -\frac {F^a\,b^5\,{\ln \relax (F)}^5\,\mathrm {expint}\left (-b\,\ln \relax (F)\,{\left (c+d\,x\right )}^2\right )}{240\,d}-\frac {F^a\,F^{b\,{\left (c+d\,x\right )}^2}\,b^5\,{\ln \relax (F)}^5\,\left (\frac {1}{120\,b\,\ln \relax (F)\,{\left (c+d\,x\right )}^2}+\frac {1}{120\,b^2\,{\ln \relax (F)}^2\,{\left (c+d\,x\right )}^4}+\frac {1}{60\,b^3\,{\ln \relax (F)}^3\,{\left (c+d\,x\right )}^6}+\frac {1}{20\,b^4\,{\ln \relax (F)}^4\,{\left (c+d\,x\right )}^8}+\frac {1}{5\,b^5\,{\ln \relax (F)}^5\,{\left (c+d\,x\right )}^{10}}\right )}{2\,d} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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