Optimal. Leaf size=201 \[ -\frac{3}{80} (1-2 x)^{3/2} (3 x+2)^3 (5 x+3)^{7/2}-\frac{1419 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{7/2}}{11200}-\frac{3 (1-2 x)^{3/2} (522420 x+899099) (5 x+3)^{7/2}}{1280000}-\frac{135817609 (1-2 x)^{3/2} (5 x+3)^{5/2}}{20480000}-\frac{1493993699 (1-2 x)^{3/2} (5 x+3)^{3/2}}{49152000}-\frac{16433930689 (1-2 x)^{3/2} \sqrt{5 x+3}}{131072000}+\frac{180773237579 \sqrt{1-2 x} \sqrt{5 x+3}}{1310720000}+\frac{1988505613369 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{1310720000 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.276063, antiderivative size = 201, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{3}{80} (1-2 x)^{3/2} (3 x+2)^3 (5 x+3)^{7/2}-\frac{1419 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{7/2}}{11200}-\frac{3 (1-2 x)^{3/2} (522420 x+899099) (5 x+3)^{7/2}}{1280000}-\frac{135817609 (1-2 x)^{3/2} (5 x+3)^{5/2}}{20480000}-\frac{1493993699 (1-2 x)^{3/2} (5 x+3)^{3/2}}{49152000}-\frac{16433930689 (1-2 x)^{3/2} \sqrt{5 x+3}}{131072000}+\frac{180773237579 \sqrt{1-2 x} \sqrt{5 x+3}}{1310720000}+\frac{1988505613369 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{1310720000 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 26.9205, size = 187, normalized size = 0.93 \[ - \frac{3 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{3} \left (5 x + 3\right )^{\frac{7}{2}}}{80} - \frac{1419 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{\frac{7}{2}}}{11200} - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{7}{2}} \left (\frac{41140575 x}{2} + \frac{283216185}{8}\right )}{16800000} + \frac{135817609 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{7}{2}}}{51200000} - \frac{1493993699 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}}}{614400000} - \frac{16433930689 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{983040000} - \frac{180773237579 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{1310720000} + \frac{1988505613369 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{13107200000} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**(5/2)*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.160535, size = 85, normalized size = 0.42 \[ \frac{10 \sqrt{1-2 x} \sqrt{5 x+3} \left (6967296000000 x^7+30838579200000 x^6+57746856960000 x^5+58346097408000 x^4+32457421737600 x^3+6882844528480 x^2-3991703112140 x-5973304472091\right )-41758617880749 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{275251200000} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(5/2),x]
[Out]
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Maple [A] time = 0.017, size = 172, normalized size = 0.9 \[{\frac{1}{550502400000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 139345920000000\,{x}^{7}\sqrt{-10\,{x}^{2}-x+3}+616771584000000\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}+1154937139200000\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}+1166921948160000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}+649148434752000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+137656890569600\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+41758617880749\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -79834062242800\,x\sqrt{-10\,{x}^{2}-x+3}-119466089441820\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^(5/2)*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.48985, size = 186, normalized size = 0.93 \[ -\frac{405}{16} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{5} - \frac{49059}{448} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{4} - \frac{739881}{3584} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{3} - \frac{80346831}{358400} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{2} - \frac{4513921183}{28672000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x - \frac{26326737569}{344064000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{16433930689}{65536000} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{1988505613369}{26214400000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) + \frac{16433930689}{1310720000} \, \sqrt{-10 \, x^{2} - x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219694, size = 117, normalized size = 0.58 \[ \frac{1}{550502400000} \, \sqrt{10}{\left (2 \, \sqrt{10}{\left (6967296000000 \, x^{7} + 30838579200000 \, x^{6} + 57746856960000 \, x^{5} + 58346097408000 \, x^{4} + 32457421737600 \, x^{3} + 6882844528480 \, x^{2} - 3991703112140 \, x - 5973304472091\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 41758617880749 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^4*sqrt(-2*x + 1),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((2+3*x)**4*(3+5*x)**(5/2)*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.276704, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="giac")
[Out]