Optimal. Leaf size=21 \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0301171, antiderivative size = 21, 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 \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 5.29214, size = 17, normalized size = 0.81 \[ - \frac{7 \log{\left (- 2 x + 1 \right )}}{22} + \frac{\log{\left (5 x + 3 \right )}}{55} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(1-2*x)/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0066902, size = 21, normalized size = 1. \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/((1 - 2*x)*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.008, size = 18, normalized size = 0.9 \[{\frac{\ln \left ( 3+5\,x \right ) }{55}}-{\frac{7\,\ln \left ( -1+2\,x \right ) }{22}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(1-2*x)/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34146, size = 23, normalized size = 1.1 \[ \frac{1}{55} \, \log \left (5 \, x + 3\right ) - \frac{7}{22} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212682, size = 23, normalized size = 1.1 \[ \frac{1}{55} \, \log \left (5 \, x + 3\right ) - \frac{7}{22} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.252636, size = 17, normalized size = 0.81 \[ - \frac{7 \log{\left (x - \frac{1}{2} \right )}}{22} + \frac{\log{\left (x + \frac{3}{5} \right )}}{55} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(1-2*x)/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.209539, size = 26, normalized size = 1.24 \[ \frac{1}{55} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7}{22} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)*(2*x - 1)),x, algorithm="giac")
[Out]