Optimal. Leaf size=19 \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]
[Out]
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Rubi [A] time = 0.0543293, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]
Antiderivative was successfully verified.
[In] Int[(4 + 3*x^4)/(5*x + 2*x^5),x]
[Out]
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Rubi in Sympy [A] time = 8.28586, size = 17, normalized size = 0.89 \[ \frac{\log{\left (x^{4} \right )}}{5} + \frac{7 \log{\left (2 x^{4} + 5 \right )}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*x**4+4)/(2*x**5+5*x),x)
[Out]
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Mathematica [A] time = 0.008972, size = 19, normalized size = 1. \[ \frac{7}{40} \log \left (2 x^4+5\right )+\frac{4 \log (x)}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(4 + 3*x^4)/(5*x + 2*x^5),x]
[Out]
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Maple [A] time = 0.007, size = 16, normalized size = 0.8 \[{\frac{4\,\ln \left ( x \right ) }{5}}+{\frac{7\,\ln \left ( 2\,{x}^{4}+5 \right ) }{40}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*x^4+4)/(2*x^5+5*x),x)
[Out]
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Maxima [A] time = 1.51112, size = 20, normalized size = 1.05 \[ \frac{7}{40} \, \log \left (2 \, x^{4} + 5\right ) + \frac{4}{5} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206577, size = 20, normalized size = 1.05 \[ \frac{7}{40} \, \log \left (2 \, x^{4} + 5\right ) + \frac{4}{5} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.108864, size = 17, normalized size = 0.89 \[ \frac{4 \log{\left (x \right )}}{5} + \frac{7 \log{\left (2 x^{4} + 5 \right )}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x**4+4)/(2*x**5+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.224476, size = 23, normalized size = 1.21 \[ \frac{7}{40} \,{\rm ln}\left (2 \, x^{4} + 5\right ) + \frac{1}{5} \,{\rm ln}\left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^4 + 4)/(2*x^5 + 5*x),x, algorithm="giac")
[Out]