Optimal. Leaf size=31 \[ -\frac{b^5 F^a \log ^5(F) \text{Gamma}\left (-5,-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
[Out]
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Rubi [A] time = 0.0754626, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ -\frac{b^5 F^a \log ^5(F) \text{Gamma}\left (-5,-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)^2)*(c + d*x)^9,x]
[Out]
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Rubi in Sympy [A] time = 6.35865, size = 32, normalized size = 1.03 \[ - \frac{F^{a} b^{5} \Gamma{\left (-5,- \frac{b \log{\left (F \right )}}{\left (c + d x\right )^{2}} \right )} \log{\left (F \right )}^{5}}{2 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)**2)*(d*x+c)**9,x)
[Out]
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Mathematica [B] time = 0.12449, size = 112, normalized size = 3.61 \[ \frac{F^a \left ((c+d x)^2 F^{\frac{b}{(c+d x)^2}} \left (b^4 \log ^4(F)+b^3 \log ^3(F) (c+d x)^2+2 b^2 \log ^2(F) (c+d x)^4+6 b \log (F) (c+d x)^6+24 (c+d x)^8\right )-b^5 \log ^5(F) \text{ExpIntegralEi}\left (\frac{b \log (F)}{(c+d x)^2}\right )\right )}{240 d} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^9,x]
[Out]
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Maple [B] time = 0.09, size = 961, normalized size = 31. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)^2)*(d*x+c)^9,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \frac{1}{240} \,{\left (24 \, F^{a} d^{9} x^{10} + 240 \, F^{a} c d^{8} x^{9} + 6 \,{\left (180 \, F^{a} c^{2} d^{7} + F^{a} b d^{7} \log \left (F\right )\right )} x^{8} + 48 \,{\left (60 \, F^{a} c^{3} d^{6} + F^{a} b c d^{6} \log \left (F\right )\right )} x^{7} + 2 \,{\left (2520 \, F^{a} c^{4} d^{5} + 84 \, F^{a} b c^{2} d^{5} \log \left (F\right ) + F^{a} b^{2} d^{5} \log \left (F\right )^{2}\right )} x^{6} + 12 \,{\left (504 \, F^{a} c^{5} d^{4} + 28 \, F^{a} b c^{3} d^{4} \log \left (F\right ) + F^{a} b^{2} c d^{4} \log \left (F\right )^{2}\right )} x^{5} +{\left (5040 \, F^{a} c^{6} d^{3} + 420 \, F^{a} b c^{4} d^{3} \log \left (F\right ) + 30 \, F^{a} b^{2} c^{2} d^{3} \log \left (F\right )^{2} + F^{a} b^{3} d^{3} \log \left (F\right )^{3}\right )} x^{4} + 4 \,{\left (720 \, F^{a} c^{7} d^{2} + 84 \, F^{a} b c^{5} d^{2} \log \left (F\right ) + 10 \, F^{a} b^{2} c^{3} d^{2} \log \left (F\right )^{2} + F^{a} b^{3} c d^{2} \log \left (F\right )^{3}\right )} x^{3} +{\left (1080 \, F^{a} c^{8} d + 168 \, F^{a} b c^{6} d \log \left (F\right ) + 30 \, F^{a} b^{2} c^{4} d \log \left (F\right )^{2} + 6 \, F^{a} b^{3} c^{2} d \log \left (F\right )^{3} + F^{a} b^{4} d \log \left (F\right )^{4}\right )} x^{2} + 2 \,{\left (120 \, F^{a} c^{9} + 24 \, F^{a} b c^{7} \log \left (F\right ) + 6 \, F^{a} b^{2} c^{5} \log \left (F\right )^{2} + 2 \, F^{a} b^{3} c^{3} \log \left (F\right )^{3} + F^{a} b^{4} c \log \left (F\right )^{4}\right )} x\right )} F^{\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}} + \int \frac{{\left (F^{a} b^{5} d^{2} x^{2} \log \left (F\right )^{5} + 2 \, F^{a} b^{5} c d x \log \left (F\right )^{5} - 24 \, F^{a} b c^{10} \log \left (F\right ) - 6 \, F^{a} b^{2} c^{8} \log \left (F\right )^{2} - 2 \, F^{a} b^{3} c^{6} \log \left (F\right )^{3} - F^{a} b^{4} c^{4} \log \left (F\right )^{4}\right )} F^{\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}}}{120 \,{\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^9*F^(a + b/(d*x + c)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.260159, size = 628, normalized size = 20.26 \[ -\frac{F^{a} b^{5}{\rm Ei}\left (\frac{b \log \left (F\right )}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right ) \log \left (F\right )^{5} -{\left (24 \, d^{10} x^{10} + 240 \, c d^{9} x^{9} + 1080 \, c^{2} d^{8} x^{8} + 2880 \, c^{3} d^{7} x^{7} + 5040 \, c^{4} d^{6} x^{6} + 6048 \, c^{5} d^{5} x^{5} + 5040 \, c^{6} d^{4} x^{4} + 2880 \, c^{7} d^{3} x^{3} + 1080 \, c^{8} d^{2} x^{2} + 240 \, c^{9} d x + 24 \, c^{10} +{\left (b^{4} d^{2} x^{2} + 2 \, b^{4} c d x + b^{4} c^{2}\right )} \log \left (F\right )^{4} +{\left (b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right )} \log \left (F\right )^{3} + 2 \,{\left (b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + 20 \, b^{2} c^{3} d^{3} x^{3} + 15 \, b^{2} c^{4} d^{2} x^{2} + 6 \, b^{2} c^{5} d x + b^{2} c^{6}\right )} \log \left (F\right )^{2} + 6 \,{\left (b d^{8} x^{8} + 8 \, b c d^{7} x^{7} + 28 \, b c^{2} d^{6} x^{6} + 56 \, b c^{3} d^{5} x^{5} + 70 \, b c^{4} d^{4} x^{4} + 56 \, b c^{5} d^{3} x^{3} + 28 \, b c^{6} d^{2} x^{2} + 8 \, b c^{7} d x + b c^{8}\right )} \log \left (F\right )\right )} F^{\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}}}{240 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^9*F^(a + b/(d*x + c)^2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b/(d*x+c)**2)*(d*x+c)**9,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{9} F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^9*F^(a + b/(d*x + c)^2),x, algorithm="giac")
[Out]