Optimal. Leaf size=98 \[ \frac{352}{823543 (1-2 x)}-\frac{2608}{823543 (3 x+2)}-\frac{520}{117649 (3 x+2)^2}-\frac{388}{50421 (3 x+2)^3}-\frac{32}{2401 (3 x+2)^4}-\frac{31}{1715 (3 x+2)^5}+\frac{1}{294 (3 x+2)^6}-\frac{128 \log (1-2 x)}{117649}+\frac{128 \log (3 x+2)}{117649} \]
[Out]
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Rubi [A] time = 0.110494, antiderivative size = 98, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{352}{823543 (1-2 x)}-\frac{2608}{823543 (3 x+2)}-\frac{520}{117649 (3 x+2)^2}-\frac{388}{50421 (3 x+2)^3}-\frac{32}{2401 (3 x+2)^4}-\frac{31}{1715 (3 x+2)^5}+\frac{1}{294 (3 x+2)^6}-\frac{128 \log (1-2 x)}{117649}+\frac{128 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^7),x]
[Out]
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Rubi in Sympy [A] time = 13.9562, size = 83, normalized size = 0.85 \[ - \frac{128 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{128 \log{\left (3 x + 2 \right )}}{117649} - \frac{2608}{823543 \left (3 x + 2\right )} - \frac{520}{117649 \left (3 x + 2\right )^{2}} - \frac{388}{50421 \left (3 x + 2\right )^{3}} - \frac{32}{2401 \left (3 x + 2\right )^{4}} - \frac{31}{1715 \left (3 x + 2\right )^{5}} + \frac{1}{294 \left (3 x + 2\right )^{6}} + \frac{352}{823543 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)**2/(2+3*x)**7,x)
[Out]
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Mathematica [A] time = 0.06382, size = 67, normalized size = 0.68 \[ \frac{-\frac{7 \left (311040 x^6+1062720 x^5+1398240 x^4+807480 x^3+84708 x^2-132772 x-49131\right )}{(2 x-1) (3 x+2)^6}-1280 \log (1-2 x)+1280 \log (6 x+4)}{1176490} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^7),x]
[Out]
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Maple [A] time = 0.018, size = 81, normalized size = 0.8 \[{\frac{1}{294\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{31}{1715\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{32}{2401\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{388}{50421\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{520}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2608}{1647086+2470629\,x}}+{\frac{128\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{352}{-823543+1647086\,x}}-{\frac{128\,\ln \left ( -1+2\,x \right ) }{117649}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)^2/(2+3*x)^7,x)
[Out]
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Maxima [A] time = 1.34233, size = 109, normalized size = 1.11 \[ -\frac{311040 \, x^{6} + 1062720 \, x^{5} + 1398240 \, x^{4} + 807480 \, x^{3} + 84708 \, x^{2} - 132772 \, x - 49131}{168070 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} + \frac{128}{117649} \, \log \left (3 \, x + 2\right ) - \frac{128}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^7*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219996, size = 189, normalized size = 1.93 \[ -\frac{2177280 \, x^{6} + 7439040 \, x^{5} + 9787680 \, x^{4} + 5652360 \, x^{3} + 592956 \, x^{2} - 1280 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (3 \, x + 2\right ) + 1280 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (2 \, x - 1\right ) - 929404 \, x - 343917}{1176490 \,{\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^7*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.564433, size = 80, normalized size = 0.82 \[ - \frac{311040 x^{6} + 1062720 x^{5} + 1398240 x^{4} + 807480 x^{3} + 84708 x^{2} - 132772 x - 49131}{245046060 x^{7} + 857661210 x^{6} + 1143548280 x^{5} + 635304600 x^{4} - 169414560 x^{2} - 75295360 x - 10756480} - \frac{128 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{128 \log{\left (x + \frac{2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)**2/(2+3*x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.212518, size = 117, normalized size = 1.19 \[ -\frac{352}{823543 \,{\left (2 \, x - 1\right )}} + \frac{288 \,{\left (\frac{1446039}{2 \, x - 1} + \frac{7393365}{{\left (2 \, x - 1\right )}^{2}} + \frac{19147975}{{\left (2 \, x - 1\right )}^{3}} + \frac{25210500}{{\left (2 \, x - 1\right )}^{4}} + \frac{13529635}{{\left (2 \, x - 1\right )}^{5}} + 114291\right )}}{28824005 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{6}} + \frac{128}{117649} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^7*(2*x - 1)^2),x, algorithm="giac")
[Out]