Optimal. Leaf size=23 \[ \frac{1}{7} \log \left (\frac{1}{x}+5\right )-\frac{1}{7} \log \left (\frac{2}{x}+3\right ) \]
[Out]
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Rubi [A] time = 0.0302982, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{1}{7} \log \left (\frac{1}{x}+5\right )-\frac{1}{7} \log \left (\frac{2}{x}+3\right ) \]
Antiderivative was successfully verified.
[In] Int[1/((15 + 2/x^2 + 13/x)*x^2),x]
[Out]
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Rubi in Sympy [A] time = 6.82851, size = 15, normalized size = 0.65 \[ - \frac{\log{\left (3 + \frac{2}{x} \right )}}{7} + \frac{\log{\left (5 + \frac{1}{x} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(15+2/x**2+13/x)/x**2,x)
[Out]
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Mathematica [A] time = 0.00448552, size = 21, normalized size = 0.91 \[ \frac{1}{7} \log (5 x+1)-\frac{1}{7} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/((15 + 2/x^2 + 13/x)*x^2),x]
[Out]
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Maple [A] time = 0.007, size = 18, normalized size = 0.8 \[{\frac{\ln \left ( 1+5\,x \right ) }{7}}-{\frac{\ln \left ( 2+3\,x \right ) }{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(15+2/x^2+13/x)/x^2,x)
[Out]
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Maxima [A] time = 0.750124, size = 23, normalized size = 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/(x^2*(13/x + 2/x^2 + 15)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246921, size = 23, normalized size = 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/(x^2*(13/x + 2/x^2 + 15)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.216806, size = 15, normalized size = 0.65 \[ \frac{\log{\left (x + \frac{1}{5} \right )}}{7} - \frac{\log{\left (x + \frac{2}{3} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(15+2/x**2+13/x)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.301019, size = 26, normalized size = 1.13 \[ \frac{1}{7} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{1}{7} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^2*(13/x + 2/x^2 + 15)),x, algorithm="giac")
[Out]