Optimal. Leaf size=69 \[ \frac{2187 x^4}{400}+\frac{16281 x^3}{500}+\frac{1974861 x^2}{20000}+\frac{6156243 x}{25000}+\frac{823543}{7744 (1-2 x)}-\frac{1}{1890625 (5 x+3)}+\frac{18941489 \log (1-2 x)}{85184}+\frac{47 \log (5 x+3)}{4159375} \]
[Out]
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Rubi [A] time = 0.0797241, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{2187 x^4}{400}+\frac{16281 x^3}{500}+\frac{1974861 x^2}{20000}+\frac{6156243 x}{25000}+\frac{823543}{7744 (1-2 x)}-\frac{1}{1890625 (5 x+3)}+\frac{18941489 \log (1-2 x)}{85184}+\frac{47 \log (5 x+3)}{4159375} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2187 x^{4}}{400} + \frac{16281 x^{3}}{500} + \frac{18941489 \log{\left (- 2 x + 1 \right )}}{85184} + \frac{47 \log{\left (5 x + 3 \right )}}{4159375} + \int \frac{6156243}{25000}\, dx + \frac{1974861 \int x\, dx}{10000} - \frac{1}{1890625 \left (5 x + 3\right )} + \frac{823543}{7744 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**7/(1-2*x)**2/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0645156, size = 74, normalized size = 1.07 \[ \frac{-\frac{11 (64339297003 x+38603578061)}{10 x^2+x-3}+89842500 (3 x+2)^4+886446000 (3 x+2)^3+7128103950 (3 x+2)^2+67228064640 (3 x+2)+295960765625 \log (3-6 x)+15040 \log (-3 (5 x+3))}{1331000000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 54, normalized size = 0.8 \[{\frac{2187\,{x}^{4}}{400}}+{\frac{16281\,{x}^{3}}{500}}+{\frac{1974861\,{x}^{2}}{20000}}+{\frac{6156243\,x}{25000}}-{\frac{1}{5671875+9453125\,x}}+{\frac{47\,\ln \left ( 3+5\,x \right ) }{4159375}}-{\frac{823543}{-7744+15488\,x}}+{\frac{18941489\,\ln \left ( -1+2\,x \right ) }{85184}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^7/(1-2*x)^2/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.32986, size = 70, normalized size = 1.01 \[ \frac{2187}{400} \, x^{4} + \frac{16281}{500} \, x^{3} + \frac{1974861}{20000} \, x^{2} + \frac{6156243}{25000} \, x - \frac{64339297003 \, x + 38603578061}{121000000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{47}{4159375} \, \log \left (5 \, x + 3\right ) + \frac{18941489}{85184} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210918, size = 100, normalized size = 1.45 \[ \frac{72772425000 \, x^{6} + 440677462500 \, x^{5} + 1335778290000 \, x^{4} + 3278990706750 \, x^{3} - 66522621330 \, x^{2} + 15040 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 295960765625 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 1691007398993 \, x - 424639358671}{1331000000 \,{\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.414258, size = 60, normalized size = 0.87 \[ \frac{2187 x^{4}}{400} + \frac{16281 x^{3}}{500} + \frac{1974861 x^{2}}{20000} + \frac{6156243 x}{25000} - \frac{64339297003 x + 38603578061}{1210000000 x^{2} + 121000000 x - 363000000} + \frac{18941489 \log{\left (x - \frac{1}{2} \right )}}{85184} + \frac{47 \log{\left (x + \frac{3}{5} \right )}}{4159375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**7/(1-2*x)**2/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21207, size = 139, normalized size = 2.01 \[ -\frac{{\left (5 \, x + 3\right )}^{4}{\left (\frac{142957386}{5 \, x + 3} + \frac{1626867990}{{\left (5 \, x + 3\right )}^{2}} + \frac{26903695995}{{\left (5 \, x + 3\right )}^{3}} - \frac{295961527385}{{\left (5 \, x + 3\right )}^{4}} + 11643588\right )}}{665500000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{1890625 \,{\left (5 \, x + 3\right )}} - \frac{44471943}{200000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{18941489}{85184} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7/((5*x + 3)^2*(2*x - 1)^2),x, algorithm="giac")
[Out]