Optimal. Leaf size=65 \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]
[Out]
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Rubi [A] time = 0.0667264, antiderivative size = 65, 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 \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^5),x]
[Out]
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Rubi in Sympy [A] time = 10.2171, size = 56, normalized size = 0.86 \[ - \frac{2662 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{2662 \log{\left (3 x + 2 \right )}}{16807} - \frac{1331}{2401 \left (3 x + 2\right )} + \frac{3469}{18522 \left (3 x + 2\right )^{2}} - \frac{103}{3969 \left (3 x + 2\right )^{3}} + \frac{1}{756 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.055118, size = 47, normalized size = 0.72 \[ \frac{2 \left (-\frac{7 \left (11643588 x^3+21975894 x^2+13836972 x+2906507\right )}{8 (3 x+2)^4}-107811 \log (1-2 x)+107811 \log (6 x+4)\right )}{1361367} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^5),x]
[Out]
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Maple [A] time = 0.013, size = 54, normalized size = 0.8 \[{\frac{1}{756\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{103}{3969\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{3469}{18522\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1331}{4802+7203\,x}}+{\frac{2662\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{2662\,\ln \left ( -1+2\,x \right ) }{16807}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.34419, size = 76, normalized size = 1.17 \[ -\frac{11643588 \, x^{3} + 21975894 \, x^{2} + 13836972 \, x + 2906507}{777924 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2662}{16807} \, \log \left (3 \, x + 2\right ) - \frac{2662}{16807} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)^5*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213562, size = 128, normalized size = 1.97 \[ -\frac{81505116 \, x^{3} + 153831258 \, x^{2} - 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 96858804 \, x + 20345549}{5445468 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)^5*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.475888, size = 54, normalized size = 0.83 \[ - \frac{11643588 x^{3} + 21975894 x^{2} + 13836972 x + 2906507}{63011844 x^{4} + 168031584 x^{3} + 168031584 x^{2} + 74680704 x + 12446784} - \frac{2662 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{2662 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.212277, size = 70, normalized size = 1.08 \[ -\frac{1331}{2401 \,{\left (3 \, x + 2\right )}} + \frac{3469}{18522 \,{\left (3 \, x + 2\right )}^{2}} - \frac{103}{3969 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{756 \,{\left (3 \, x + 2\right )}^{4}} - \frac{2662}{16807} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3/((3*x + 2)^5*(2*x - 1)),x, algorithm="giac")
[Out]