Optimal. Leaf size=29 \[ -\frac{2 \tan ^{-1}\left (\frac{c-2 d x}{\sqrt{3} c}\right )}{\sqrt{3} c d} \]
[Out]
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Rubi [A] time = 0.0467412, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ -\frac{2 \tan ^{-1}\left (\frac{c-2 d x}{\sqrt{3} c}\right )}{\sqrt{3} c d} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)/(c^3 + d^3*x^3),x]
[Out]
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Rubi in Sympy [A] time = 5.16106, size = 31, normalized size = 1.07 \[ - \frac{2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \left (\frac{c}{3} - \frac{2 d x}{3}\right )}{c} \right )}}{3 c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)/(d**3*x**3+c**3),x)
[Out]
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Mathematica [A] time = 0.0186217, size = 31, normalized size = 1.07 \[ \frac{2 \tan ^{-1}\left (\frac{2 d x-c}{\sqrt{3} c}\right )}{\sqrt{3} c d} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)/(c^3 + d^3*x^3),x]
[Out]
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Maple [A] time = 0.009, size = 35, normalized size = 1.2 \[{\frac{2\,\sqrt{3}}{3\,cd}\arctan \left ({\frac{ \left ( 2\,{d}^{2}x-cd \right ) \sqrt{3}}{3\,cd}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)/(d^3*x^3+c^3),x)
[Out]
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Maxima [A] time = 1.52522, size = 46, normalized size = 1.59 \[ \frac{2 \, \sqrt{3} \arctan \left (\frac{\sqrt{3}{\left (2 \, d^{2} x - c d\right )}}{3 \, c d}\right )}{3 \, c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)/(d^3*x^3 + c^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217404, size = 38, normalized size = 1.31 \[ \frac{2 \, \sqrt{3} \arctan \left (\frac{\sqrt{3}{\left (2 \, d x - c\right )}}{3 \, c}\right )}{3 \, c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)/(d^3*x^3 + c^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.200274, size = 54, normalized size = 1.86 \[ \frac{- \frac{\sqrt{3} i \log{\left (x + \frac{- c - \sqrt{3} i c}{2 d} \right )}}{3} + \frac{\sqrt{3} i \log{\left (x + \frac{- c + \sqrt{3} i c}{2 d} \right )}}{3}}{c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)/(d**3*x**3+c**3),x)
[Out]
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GIAC/XCAS [A] time = 0.21067, size = 38, normalized size = 1.31 \[ \frac{2 \, \sqrt{3} \arctan \left (\frac{\sqrt{3}{\left (2 \, d x - c\right )}}{3 \, c}\right )}{3 \, c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)/(d^3*x^3 + c^3),x, algorithm="giac")
[Out]