Optimal. Leaf size=64 \[ \frac{404}{41503 (1-2 x)}+\frac{27}{343 (3 x+2)}+\frac{2}{539 (1-2 x)^2}-\frac{27208 \log (1-2 x)}{3195731}-\frac{1107 \log (3 x+2)}{2401}+\frac{625 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.0735967, antiderivative size = 64, 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 \[ \frac{404}{41503 (1-2 x)}+\frac{27}{343 (3 x+2)}+\frac{2}{539 (1-2 x)^2}-\frac{27208 \log (1-2 x)}{3195731}-\frac{1107 \log (3 x+2)}{2401}+\frac{625 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 10.0073, size = 53, normalized size = 0.83 \[ - \frac{27208 \log{\left (- 2 x + 1 \right )}}{3195731} - \frac{1107 \log{\left (3 x + 2 \right )}}{2401} + \frac{625 \log{\left (5 x + 3 \right )}}{1331} + \frac{27}{343 \left (3 x + 2\right )} + \frac{404}{41503 \left (- 2 x + 1\right )} + \frac{2}{539 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**3/(2+3*x)**2/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.107907, size = 57, normalized size = 0.89 \[ \frac{\frac{77 \left (10644 x^2-13010 x+4383\right )}{(1-2 x)^2 (3 x+2)}-27208 \log (5-10 x)-1473417 \log (5 (3 x+2))+1500625 \log (5 x+3)}{3195731} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.016, size = 53, normalized size = 0.8 \[{\frac{625\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27}{686+1029\,x}}-{\frac{1107\,\ln \left ( 2+3\,x \right ) }{2401}}+{\frac{2}{539\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{404}{-41503+83006\,x}}-{\frac{27208\,\ln \left ( -1+2\,x \right ) }{3195731}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^3/(2+3*x)^2/(3+5*x),x)
[Out]
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Maxima [A] time = 1.37048, size = 73, normalized size = 1.14 \[ \frac{10644 \, x^{2} - 13010 \, x + 4383}{41503 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} + \frac{625}{1331} \, \log \left (5 \, x + 3\right ) - \frac{1107}{2401} \, \log \left (3 \, x + 2\right ) - \frac{27208}{3195731} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214713, size = 132, normalized size = 2.06 \[ \frac{819588 \, x^{2} + 1500625 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1473417 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 27208 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (2 \, x - 1\right ) - 1001770 \, x + 337491}{3195731 \,{\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.539397, size = 54, normalized size = 0.84 \[ \frac{10644 x^{2} - 13010 x + 4383}{498036 x^{3} - 166012 x^{2} - 207515 x + 83006} - \frac{27208 \log{\left (x - \frac{1}{2} \right )}}{3195731} + \frac{625 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{1107 \log{\left (x + \frac{2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**3/(2+3*x)**2/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.21945, size = 89, normalized size = 1.39 \[ \frac{27}{343 \,{\left (3 \, x + 2\right )}} + \frac{24 \,{\left (\frac{938}{3 \, x + 2} - 235\right )}}{290521 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} + \frac{625}{1331} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{27208}{3195731} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]