Optimal. Leaf size=184 \[ -\frac{13 \left (3 x^2+5 x+2\right )^{9/2}}{45 (2 x+3)^9}+\frac{47 (8 x+7) \left (3 x^2+5 x+2\right )^{7/2}}{800 (2 x+3)^8}-\frac{329 (8 x+7) \left (3 x^2+5 x+2\right )^{5/2}}{96000 (2 x+3)^6}+\frac{329 (8 x+7) \left (3 x^2+5 x+2\right )^{3/2}}{1536000 (2 x+3)^4}-\frac{329 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000 (2 x+3)^2}+\frac{329 \tanh ^{-1}\left (\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right )}{40960000 \sqrt{5}} \]
[Out]
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Rubi [A] time = 0.253096, antiderivative size = 184, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 4, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.148 \[ -\frac{13 \left (3 x^2+5 x+2\right )^{9/2}}{45 (2 x+3)^9}+\frac{47 (8 x+7) \left (3 x^2+5 x+2\right )^{7/2}}{800 (2 x+3)^8}-\frac{329 (8 x+7) \left (3 x^2+5 x+2\right )^{5/2}}{96000 (2 x+3)^6}+\frac{329 (8 x+7) \left (3 x^2+5 x+2\right )^{3/2}}{1536000 (2 x+3)^4}-\frac{329 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000 (2 x+3)^2}+\frac{329 \tanh ^{-1}\left (\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right )}{40960000 \sqrt{5}} \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^10,x]
[Out]
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Rubi in Sympy [A] time = 44.751, size = 175, normalized size = 0.95 \[ - \frac{329 \sqrt{5} \operatorname{atanh}{\left (\frac{\sqrt{5} \left (- 8 x - 7\right )}{10 \sqrt{3 x^{2} + 5 x + 2}} \right )}}{204800000} - \frac{329 \left (8 x + 7\right ) \sqrt{3 x^{2} + 5 x + 2}}{20480000 \left (2 x + 3\right )^{2}} + \frac{329 \left (8 x + 7\right ) \left (3 x^{2} + 5 x + 2\right )^{\frac{3}{2}}}{1536000 \left (2 x + 3\right )^{4}} - \frac{329 \left (8 x + 7\right ) \left (3 x^{2} + 5 x + 2\right )^{\frac{5}{2}}}{96000 \left (2 x + 3\right )^{6}} + \frac{47 \left (8 x + 7\right ) \left (3 x^{2} + 5 x + 2\right )^{\frac{7}{2}}}{800 \left (2 x + 3\right )^{8}} - \frac{13 \left (3 x^{2} + 5 x + 2\right )^{\frac{9}{2}}}{45 \left (2 x + 3\right )^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**10,x)
[Out]
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Mathematica [A] time = 0.136947, size = 129, normalized size = 0.7 \[ -\frac{2961 \sqrt{5} (2 x+3)^9 \log \left (2 \sqrt{5} \sqrt{3 x^2+5 x+2}-8 x-7\right )-10 \sqrt{3 x^2+5 x+2} \left (28394496 x^8+2848109952 x^7+15895201728 x^6+38558367264 x^5+51825176720 x^4+41530110824 x^3+19810691268 x^2+5201574542 x+578701331\right )-2961 \sqrt{5} (2 x+3)^9 \log (2 x+3)}{1843200000 (2 x+3)^9} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^10,x]
[Out]
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Maple [B] time = 0.055, size = 369, normalized size = 2. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3*x^2+5*x+2)^(7/2)/(3+2*x)^10,x)
[Out]
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Maxima [A] time = 0.821149, size = 693, normalized size = 3.77 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^(7/2)*(x - 5)/(2*x + 3)^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.291793, size = 277, normalized size = 1.51 \[ \frac{\sqrt{5}{\left (4 \, \sqrt{5}{\left (28394496 \, x^{8} + 2848109952 \, x^{7} + 15895201728 \, x^{6} + 38558367264 \, x^{5} + 51825176720 \, x^{4} + 41530110824 \, x^{3} + 19810691268 \, x^{2} + 5201574542 \, x + 578701331\right )} \sqrt{3 \, x^{2} + 5 \, x + 2} + 2961 \,{\left (512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right )} \log \left (\frac{\sqrt{5}{\left (124 \, x^{2} + 212 \, x + 89\right )} + 20 \, \sqrt{3 \, x^{2} + 5 \, x + 2}{\left (8 \, x + 7\right )}}{4 \, x^{2} + 12 \, x + 9}\right )\right )}}{3686400000 \,{\left (512 \, x^{9} + 6912 \, x^{8} + 41472 \, x^{7} + 145152 \, x^{6} + 326592 \, x^{5} + 489888 \, x^{4} + 489888 \, x^{3} + 314928 \, x^{2} + 118098 \, x + 19683\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^(7/2)*(x - 5)/(2*x + 3)^10,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((5-x)*(3*x**2+5*x+2)**(7/2)/(3+2*x)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.316718, size = 760, normalized size = 4.13 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^(7/2)*(x - 5)/(2*x + 3)^10,x, algorithm="giac")
[Out]