Optimal. Leaf size=31 \[ \frac {b^4 F^a \log ^4(F) \Gamma \left (-4,-\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
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Rubi [A] time = 0.05, 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} \[ \frac {b^4 F^a \log ^4(F) \text {Gamma}\left (-4,-\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int F^{a+\frac {b}{(c+d x)^3}} (c+d x)^{11} \, dx &=\frac {b^4 F^a \Gamma \left (-4,-\frac {b \log (F)}{(c+d x)^3}\right ) \log ^4(F)}{3 d}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ \frac {b^4 F^a \log ^4(F) \Gamma \left (-4,-\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 487, normalized size = 15.71 \[ -\frac {F^{a} b^{4} {\rm Ei}\left (\frac {b \log \relax (F)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right ) \log \relax (F)^{4} - {\left (6 \, d^{12} x^{12} + 72 \, c d^{11} x^{11} + 396 \, c^{2} d^{10} x^{10} + 1320 \, c^{3} d^{9} x^{9} + 2970 \, c^{4} d^{8} x^{8} + 4752 \, c^{5} d^{7} x^{7} + 5544 \, c^{6} d^{6} x^{6} + 4752 \, c^{7} d^{5} x^{5} + 2970 \, c^{8} d^{4} x^{4} + 1320 \, c^{9} d^{3} x^{3} + 396 \, c^{10} d^{2} x^{2} + 72 \, c^{11} d x + 6 \, c^{12} + {\left (b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right )} \log \relax (F)^{3} + {\left (b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + 15 \, b^{2} c^{4} d^{2} x^{2} + 6 \, b^{2} c^{5} d x + b^{2} c^{6}\right )} \log \relax (F)^{2} + 2 \, {\left (b d^{9} x^{9} + 9 \, b c d^{8} x^{8} + 36 \, b c^{2} d^{7} x^{7} + 84 \, b c^{3} d^{6} x^{6} + 126 \, b c^{4} d^{5} x^{5} + 126 \, b c^{5} d^{4} x^{4} + 84 \, b c^{6} d^{3} x^{3} + 36 \, b c^{7} d^{2} x^{2} + 9 \, b c^{8} d x + b c^{9}\right )} \log \relax (F)\right )} F^{\frac {a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{72 \, d} \]
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 \[ \int {\left (d x + c\right )}^{11} F^{a + \frac {b}{{\left (d x + c\right )}^{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.16, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right )^{11} F^{a +\frac {b}{\left (d x +c \right )^{3}}}\, dx \]
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 \[ \frac {1}{72} \, {\left (6 \, F^{a} d^{11} x^{12} + 72 \, F^{a} c d^{10} x^{11} + 396 \, F^{a} c^{2} d^{9} x^{10} + 2 \, {\left (660 \, F^{a} c^{3} d^{8} + F^{a} b d^{8} \log \relax (F)\right )} x^{9} + 18 \, {\left (165 \, F^{a} c^{4} d^{7} + F^{a} b c d^{7} \log \relax (F)\right )} x^{8} + 72 \, {\left (66 \, F^{a} c^{5} d^{6} + F^{a} b c^{2} d^{6} \log \relax (F)\right )} x^{7} + {\left (5544 \, F^{a} c^{6} d^{5} + 168 \, F^{a} b c^{3} d^{5} \log \relax (F) + F^{a} b^{2} d^{5} \log \relax (F)^{2}\right )} x^{6} + 6 \, {\left (792 \, F^{a} c^{7} d^{4} + 42 \, F^{a} b c^{4} d^{4} \log \relax (F) + F^{a} b^{2} c d^{4} \log \relax (F)^{2}\right )} x^{5} + 3 \, {\left (990 \, F^{a} c^{8} d^{3} + 84 \, F^{a} b c^{5} d^{3} \log \relax (F) + 5 \, F^{a} b^{2} c^{2} d^{3} \log \relax (F)^{2}\right )} x^{4} + {\left (1320 \, F^{a} c^{9} d^{2} + 168 \, F^{a} b c^{6} d^{2} \log \relax (F) + 20 \, F^{a} b^{2} c^{3} d^{2} \log \relax (F)^{2} + F^{a} b^{3} d^{2} \log \relax (F)^{3}\right )} x^{3} + 3 \, {\left (132 \, F^{a} c^{10} d + 24 \, F^{a} b c^{7} d \log \relax (F) + 5 \, F^{a} b^{2} c^{4} d \log \relax (F)^{2} + F^{a} b^{3} c d \log \relax (F)^{3}\right )} x^{2} + 3 \, {\left (24 \, F^{a} c^{11} + 6 \, F^{a} b c^{8} \log \relax (F) + 2 \, F^{a} b^{2} c^{5} \log \relax (F)^{2} + F^{a} b^{3} c^{2} \log \relax (F)^{3}\right )} x\right )} F^{\frac {b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}} + \int -\frac {{\left (6 \, F^{a} b c^{12} \log \relax (F) - F^{a} b^{4} d^{3} x^{3} \log \relax (F)^{4} + 2 \, F^{a} b^{2} c^{9} \log \relax (F)^{2} - 3 \, F^{a} b^{4} c d^{2} x^{2} \log \relax (F)^{4} + F^{a} b^{3} c^{6} \log \relax (F)^{3} - 3 \, F^{a} b^{4} c^{2} d x \log \relax (F)^{4}\right )} F^{\frac {b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{24 \, {\left (d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.83, size = 120, normalized size = 3.87 \[ \frac {F^a\,b^4\,{\ln \relax (F)}^4\,\mathrm {expint}\left (-\frac {b\,\ln \relax (F)}{{\left (c+d\,x\right )}^3}\right )}{72\,d}+\frac {F^a\,F^{\frac {b}{{\left (c+d\,x\right )}^3}}\,b^4\,{\ln \relax (F)}^4\,\left (\frac {{\left (c+d\,x\right )}^3}{24\,b\,\ln \relax (F)}+\frac {{\left (c+d\,x\right )}^6}{24\,b^2\,{\ln \relax (F)}^2}+\frac {{\left (c+d\,x\right )}^9}{12\,b^3\,{\ln \relax (F)}^3}+\frac {{\left (c+d\,x\right )}^{12}}{4\,b^4\,{\ln \relax (F)}^4}\right )}{3\,d} \]
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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