Optimal. Leaf size=249 \[ \frac{2}{65} (1-2 x)^{5/2} (3 x+2)^{3/2} (5 x+3)^{5/2}+\frac{106 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{5/2}}{3575}+\frac{8318 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{482625}+\frac{25603 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{1876875}-\frac{6794792 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{84459375}-\frac{923943703 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{1520268750}-\frac{923943703 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{691031250 \sqrt{33}}-\frac{30660308017 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{691031250 \sqrt{33}} \]
[Out]
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Rubi [A] time = 0.56147, antiderivative size = 249, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 5, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.179 \[ \frac{2}{65} (1-2 x)^{5/2} (3 x+2)^{3/2} (5 x+3)^{5/2}+\frac{106 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{5/2}}{3575}+\frac{8318 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{482625}+\frac{25603 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{5/2}}{1876875}-\frac{6794792 \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}}{84459375}-\frac{923943703 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}}{1520268750}-\frac{923943703 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{691031250 \sqrt{33}}-\frac{30660308017 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{691031250 \sqrt{33}} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 54.268, size = 230, normalized size = 0.92 \[ \frac{2 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (3 x + 2\right )^{\frac{5}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{39} - \frac{181 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (3 x + 2\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{1287} + \frac{10496 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{57915} + \frac{1087234 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{6081075} - \frac{18399116 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{152026875} - \frac{880870681 \sqrt{- 2 x + 1} \sqrt{3 x + 2} \sqrt{5 x + 3}}{1520268750} - \frac{30660308017 \sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{22804031250} - \frac{923943703 \sqrt{35} F\left (\operatorname{asin}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}\middle | \frac{33}{35}\right )}{24186093750} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(2+3*x)**(3/2)*(3+5*x)**(3/2),x)
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Mathematica [A] time = 0.398959, size = 112, normalized size = 0.45 \[ \frac{15 \sqrt{2-4 x} \sqrt{3 x+2} \sqrt{5 x+3} \left (14033250000 x^5+5400675000 x^4-13684072500 x^3-3707642250 x^2+5290733520 x+1020785999\right )-30830473835 F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )+61320616034 E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )}{22804031250 \sqrt{2}} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2),x]
[Out]
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Maple [C] time = 0.016, size = 189, normalized size = 0.8 \[{\frac{1}{1368241875000\,{x}^{3}+1048985437500\,{x}^{2}-319256437500\,x-273648375000}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( 12629925000000\,{x}^{8}+14543550000000\,{x}^{7}-11536182000000\,{x}^{6}+30830473835\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) -61320616034\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) -16439014800000\,{x}^{5}+4104920740500\,{x}^{4}+7811051450400\,{x}^{3}+260663905110\,{x}^{2}-1166697093390\,x-183741479820 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (3 \, x + 2\right )}^{\frac{3}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^(3/2)*(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^(3/2)*(-2*x + 1)^(5/2),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((1-2*x)**(5/2)*(2+3*x)**(3/2)*(3+5*x)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (3 \, x + 2\right )}^{\frac{3}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^(3/2)*(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]