Optimal. Leaf size=31 \[ -\frac {b^4 F^a \Gamma \left (-4,-b (c+d x)^2 \log (F)\right ) \log ^4(F)}{2 d} \]
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Rubi [A]
time = 0.04, 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 = {2250}
\begin {gather*} -\frac {b^4 F^a \log ^4(F) \text {Gamma}\left (-4,-b \log (F) (c+d x)^2\right )}{2 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 2250
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 = 0.17, size = 31, normalized size = 1.00 \begin {gather*} -\frac {b^4 F^a \Gamma \left (-4,-b (c+d x)^2 \log (F)\right ) \log ^4(F)}{2 d} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(151\) vs.
\(2(29)=58\).
time = 0.11, size = 152, normalized size = 4.90
method | result | size |
risch | \(-\frac {F^{b \left (d x +c \right )^{2}} F^{a}}{8 d \left (d x +c \right )^{8}}-\frac {b \ln \left (F \right ) F^{b \left (d x +c \right )^{2}} F^{a}}{24 d \left (d x +c \right )^{6}}-\frac {b^{2} \ln \left (F \right )^{2} F^{b \left (d x +c \right )^{2}} F^{a}}{48 d \left (d x +c \right )^{4}}-\frac {b^{3} \ln \left (F \right )^{3} F^{b \left (d x +c \right )^{2}} F^{a}}{48 d \left (d x +c \right )^{2}}-\frac {b^{4} \ln \left (F \right )^{4} F^{a} \expIntegral \left (1, -b \left (d x +c \right )^{2} \ln \left (F \right )\right )}{48 d}\) | \(152\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 430 vs.
\(2 (29) = 58\).
time = 0.08, size = 430, normalized size = 13.87 \begin {gather*} \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 \left (F\right )\right ) \log \left (F\right )^{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 \left (F\right )^{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 \left (F\right )^{2} + 2 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \left (F\right ) + 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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} -\frac {F^a\,b^4\,{\ln \left (F\right )}^4\,\mathrm {expint}\left (-b\,\ln \left (F\right )\,{\left (c+d\,x\right )}^2\right )}{48\,d}-\frac {F^a\,F^{b\,{\left (c+d\,x\right )}^2}\,b^4\,{\ln \left (F\right )}^4\,\left (\frac {1}{24\,b\,\ln \left (F\right )\,{\left (c+d\,x\right )}^2}+\frac {1}{24\,b^2\,{\ln \left (F\right )}^2\,{\left (c+d\,x\right )}^4}+\frac {1}{12\,b^3\,{\ln \left (F\right )}^3\,{\left (c+d\,x\right )}^6}+\frac {1}{4\,b^4\,{\ln \left (F\right )}^4\,{\left (c+d\,x\right )}^8}\right )}{2\,d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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