Optimal. Leaf size=31 \[ -\frac {b^4 F^a \log ^4(F) \Gamma \left (-4,-b (c+d x)^2 \log (F)\right )}{2 d} \]
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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} \[ -\frac {b^4 F^a \log ^4(F) \text {Gamma}\left (-4,-b \log (F) (c+d x)^2\right )}{2 d} \]
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*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ -\frac {b^4 F^a \log ^4(F) \Gamma \left (-4,-b (c+d x)^2 \log (F)\right )}{2 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 430, normalized size = 13.87 \[ \frac {{\left (b^{4} d^{8} x^{8} + 8 \, b^{4} c d^{7} x^{7} + 28 \, b^{4} c^{2} d^{6} x^{6} + 56 \, b^{4} c^{3} d^{5} x^{5} + 70 \, b^{4} c^{4} d^{4} x^{4} + 56 \, b^{4} c^{5} d^{3} x^{3} + 28 \, b^{4} c^{6} d^{2} x^{2} + 8 \, b^{4} c^{7} d x + b^{4} c^{8}\right )} F^{a} {\rm Ei}\left ({\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \relax (F)\right ) \log \relax (F)^{4} - {\left ({\left (b^{3} d^{6} x^{6} + 6 \, b^{3} c d^{5} x^{5} + 15 \, b^{3} c^{2} d^{4} x^{4} + 20 \, b^{3} c^{3} d^{3} x^{3} + 15 \, b^{3} c^{4} d^{2} x^{2} + 6 \, b^{3} c^{5} d x + b^{3} c^{6}\right )} \log \relax (F)^{3} + {\left (b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right )} \log \relax (F)^{2} + 2 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \relax (F) + 6\right )} F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{48 \, {\left (d^{9} x^{8} + 8 \, c d^{8} x^{7} + 28 \, c^{2} d^{7} x^{6} + 56 \, c^{3} d^{6} x^{5} + 70 \, c^{4} d^{5} x^{4} + 56 \, c^{5} d^{4} x^{3} + 28 \, c^{6} d^{3} x^{2} + 8 \, c^{7} d^{2} x + c^{8} d\right )}} \]
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 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.12, size = 152, normalized size = 4.90 \[ -\frac {b^{4} F^{a} \Ei \left (1, -\left (d x +c \right )^{2} b \ln \relax (F )\right ) \ln \relax (F )^{4}}{48 d}-\frac {b^{3} F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )^{3}}{48 \left (d x +c \right )^{2} d}-\frac {b^{2} F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )^{2}}{48 \left (d x +c \right )^{4} d}-\frac {b \,F^{a} F^{\left (d x +c \right )^{2} b} \ln \relax (F )}{24 \left (d x +c \right )^{6} d}-\frac {F^{a} F^{\left (d x +c \right )^{2} b}}{8 \left (d x +c \right )^{8} d} \]
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 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{{\left (d x + c\right )}^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.81, size = 120, normalized size = 3.87 \[ -\frac {F^a\,b^4\,{\ln \relax (F)}^4\,\mathrm {expint}\left (-b\,\ln \relax (F)\,{\left (c+d\,x\right )}^2\right )}{48\,d}-\frac {F^a\,F^{b\,{\left (c+d\,x\right )}^2}\,b^4\,{\ln \relax (F)}^4\,\left (\frac {1}{24\,b\,\ln \relax (F)\,{\left (c+d\,x\right )}^2}+\frac {1}{24\,b^2\,{\ln \relax (F)}^2\,{\left (c+d\,x\right )}^4}+\frac {1}{12\,b^3\,{\ln \relax (F)}^3\,{\left (c+d\,x\right )}^6}+\frac {1}{4\,b^4\,{\ln \relax (F)}^4\,{\left (c+d\,x\right )}^8}\right )}{2\,d} \]
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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