Optimal. Leaf size=21 \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0165652, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(2 + 13*x + 15*x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.60816, size = 15, normalized size = 0.71 \[ - \frac{\log{\left (3 x + 2 \right )}}{7} + \frac{\log{\left (5 x + 1 \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(15*x**2+13*x+2),x)
[Out]
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Mathematica [A] time = 0.00389547, size = 21, normalized size = 1. \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 13*x + 15*x^2)^(-1),x]
[Out]
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Maple [A] time = 0.007, size = 18, normalized size = 0.9 \[ -{\frac{\ln \left ( 2+3\,x \right ) }{7}}+{\frac{\ln \left ( 1+5\,x \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(15*x^2+13*x+2),x)
[Out]
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Maxima [A] time = 0.828955, size = 23, normalized size = 1.1 \[ \frac{1}{7} \, \log \left (5 \, x + 1\right ) - \frac{1}{7} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^2 + 13*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211703, size = 23, normalized size = 1.1 \[ \frac{1}{7} \, \log \left (5 \, x + 1\right ) - \frac{1}{7} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^2 + 13*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.188223, size = 15, normalized size = 0.71 \[ \frac{\log{\left (x + \frac{1}{5} \right )}}{7} - \frac{\log{\left (x + \frac{2}{3} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x**2+13*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.204071, size = 26, normalized size = 1.24 \[ \frac{1}{7} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{1}{7} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15*x^2 + 13*x + 2),x, algorithm="giac")
[Out]