Optimal. Leaf size=31 \[ -\frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-\frac {b \log (F)}{(c+d x)^2}\right )}{2 d} \]
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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} \[ -\frac {b^5 F^a \log ^5(F) \text {Gamma}\left (-5,-\frac {b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int F^{a+\frac {b}{(c+d x)^2}} (c+d x)^9 \, dx &=-\frac {b^5 F^a \Gamma \left (-5,-\frac {b \log (F)}{(c+d x)^2}\right ) \log ^5(F)}{2 d}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ -\frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-\frac {b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 465, normalized size = 15.00 \[ -\frac {F^{a} b^{5} {\rm Ei}\left (\frac {b \log \relax (F)}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right ) \log \relax (F)^{5} - {\left (24 \, d^{10} x^{10} + 240 \, c d^{9} x^{9} + 1080 \, c^{2} d^{8} x^{8} + 2880 \, c^{3} d^{7} x^{7} + 5040 \, c^{4} d^{6} x^{6} + 6048 \, c^{5} d^{5} x^{5} + 5040 \, c^{6} d^{4} x^{4} + 2880 \, c^{7} d^{3} x^{3} + 1080 \, c^{8} d^{2} x^{2} + 240 \, c^{9} d x + 24 \, c^{10} + {\left (b^{4} d^{2} x^{2} + 2 \, b^{4} c d x + b^{4} c^{2}\right )} \log \relax (F)^{4} + {\left (b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right )} \log \relax (F)^{3} + 2 \, {\left (b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + 15 \, b^{2} c^{4} d^{2} x^{2} + 6 \, b^{2} c^{5} d x + b^{2} c^{6}\right )} \log \relax (F)^{2} + 6 \, {\left (b d^{8} x^{8} + 8 \, b c d^{7} x^{7} + 28 \, b c^{2} d^{6} x^{6} + 56 \, b c^{3} d^{5} x^{5} + 70 \, b c^{4} d^{4} x^{4} + 56 \, b c^{5} d^{3} x^{3} + 28 \, b c^{6} d^{2} x^{2} + 8 \, b c^{7} d x + b c^{8}\right )} \log \relax (F)\right )} F^{\frac {a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}}}{240 \, d} \]
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 \[ \int {\left (d x + c\right )}^{9} F^{a + \frac {b}{{\left (d x + c\right )}^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.13, size = 961, normalized size = 31.00 \[ \text {result too large to display} \]
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 \[ \frac {1}{240} \, {\left (24 \, F^{a} d^{9} x^{10} + 240 \, F^{a} c d^{8} x^{9} + 6 \, {\left (180 \, F^{a} c^{2} d^{7} + F^{a} b d^{7} \log \relax (F)\right )} x^{8} + 48 \, {\left (60 \, F^{a} c^{3} d^{6} + F^{a} b c d^{6} \log \relax (F)\right )} x^{7} + 2 \, {\left (2520 \, F^{a} c^{4} d^{5} + 84 \, F^{a} b c^{2} d^{5} \log \relax (F) + F^{a} b^{2} d^{5} \log \relax (F)^{2}\right )} x^{6} + 12 \, {\left (504 \, F^{a} c^{5} d^{4} + 28 \, F^{a} b c^{3} d^{4} \log \relax (F) + F^{a} b^{2} c d^{4} \log \relax (F)^{2}\right )} x^{5} + {\left (5040 \, F^{a} c^{6} d^{3} + 420 \, F^{a} b c^{4} d^{3} \log \relax (F) + 30 \, F^{a} b^{2} c^{2} d^{3} \log \relax (F)^{2} + F^{a} b^{3} d^{3} \log \relax (F)^{3}\right )} x^{4} + 4 \, {\left (720 \, F^{a} c^{7} d^{2} + 84 \, F^{a} b c^{5} d^{2} \log \relax (F) + 10 \, F^{a} b^{2} c^{3} d^{2} \log \relax (F)^{2} + F^{a} b^{3} c d^{2} \log \relax (F)^{3}\right )} x^{3} + {\left (1080 \, F^{a} c^{8} d + 168 \, F^{a} b c^{6} d \log \relax (F) + 30 \, F^{a} b^{2} c^{4} d \log \relax (F)^{2} + 6 \, F^{a} b^{3} c^{2} d \log \relax (F)^{3} + F^{a} b^{4} d \log \relax (F)^{4}\right )} x^{2} + 2 \, {\left (120 \, F^{a} c^{9} + 24 \, F^{a} b c^{7} \log \relax (F) + 6 \, F^{a} b^{2} c^{5} \log \relax (F)^{2} + 2 \, F^{a} b^{3} c^{3} \log \relax (F)^{3} + F^{a} b^{4} c \log \relax (F)^{4}\right )} x\right )} F^{\frac {b}{d^{2} x^{2} + 2 \, c d x + c^{2}}} + \int \frac {{\left (F^{a} b^{5} d^{2} x^{2} \log \relax (F)^{5} + 2 \, F^{a} b^{5} c d x \log \relax (F)^{5} - 24 \, F^{a} b c^{10} \log \relax (F) - 6 \, F^{a} b^{2} c^{8} \log \relax (F)^{2} - 2 \, F^{a} b^{3} c^{6} \log \relax (F)^{3} - F^{a} b^{4} c^{4} \log \relax (F)^{4}\right )} F^{\frac {b}{d^{2} x^{2} + 2 \, c d x + c^{2}}}}{120 \, {\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.95, size = 136, normalized size = 4.39 \[ \frac {F^a\,b^5\,{\ln \relax (F)}^5\,\mathrm {expint}\left (-\frac {b\,\ln \relax (F)}{{\left (c+d\,x\right )}^2}\right )}{240\,d}+\frac {F^a\,F^{\frac {b}{{\left (c+d\,x\right )}^2}}\,b^5\,{\ln \relax (F)}^5\,\left (\frac {{\left (c+d\,x\right )}^2}{120\,b\,\ln \relax (F)}+\frac {{\left (c+d\,x\right )}^4}{120\,b^2\,{\ln \relax (F)}^2}+\frac {{\left (c+d\,x\right )}^6}{60\,b^3\,{\ln \relax (F)}^3}+\frac {{\left (c+d\,x\right )}^8}{20\,b^4\,{\ln \relax (F)}^4}+\frac {{\left (c+d\,x\right )}^{10}}{5\,b^5\,{\ln \relax (F)}^5}\right )}{2\,d} \]
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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