Optimal. Leaf size=37 \[ \frac{1}{10} \log \left (x^{10}+x^5+2\right )-\frac{\tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
[Out]
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Rubi [A] time = 0.0685276, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.357 \[ \frac{1}{10} \log \left (x^{10}+x^5+2\right )-\frac{\tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[x^9/(2 + x^5 + x^10),x]
[Out]
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Rubi in Sympy [A] time = 8.26654, size = 34, normalized size = 0.92 \[ \frac{\log{\left (x^{10} + x^{5} + 2 \right )}}{10} - \frac{\sqrt{7} \operatorname{atan}{\left (\sqrt{7} \left (\frac{2 x^{5}}{7} + \frac{1}{7}\right ) \right )}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(x**10+x**5+2),x)
[Out]
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Mathematica [A] time = 0.0187539, size = 37, normalized size = 1. \[ \frac{1}{10} \log \left (x^{10}+x^5+2\right )-\frac{\tan ^{-1}\left (\frac{2 x^5+1}{\sqrt{7}}\right )}{5 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(2 + x^5 + x^10),x]
[Out]
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Maple [A] time = 0.004, size = 31, normalized size = 0.8 \[{\frac{\ln \left ({x}^{10}+{x}^{5}+2 \right ) }{10}}-{\frac{\sqrt{7}}{35}\arctan \left ({\frac{ \left ( 2\,{x}^{5}+1 \right ) \sqrt{7}}{7}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(x^10+x^5+2),x)
[Out]
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Maxima [A] time = 0.821823, size = 41, normalized size = 1.11 \[ -\frac{1}{35} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right ) + \frac{1}{10} \, \log \left (x^{10} + x^{5} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(x^10 + x^5 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.298392, size = 46, normalized size = 1.24 \[ \frac{1}{70} \, \sqrt{7}{\left (\sqrt{7} \log \left (x^{10} + x^{5} + 2\right ) - 2 \, \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(x^10 + x^5 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.351268, size = 37, normalized size = 1. \[ \frac{\log{\left (x^{10} + x^{5} + 2 \right )}}{10} - \frac{\sqrt{7} \operatorname{atan}{\left (\frac{2 \sqrt{7} x^{5}}{7} + \frac{\sqrt{7}}{7} \right )}}{35} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(x**10+x**5+2),x)
[Out]
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GIAC/XCAS [A] time = 0.271432, size = 41, normalized size = 1.11 \[ -\frac{1}{35} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x^{5} + 1\right )}\right ) + \frac{1}{10} \,{\rm ln}\left (x^{10} + x^{5} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(x^10 + x^5 + 2),x, algorithm="giac")
[Out]