Optimal. Leaf size=53 \[ \frac{c \log \left (c+d x^3\right )}{3 d (b c-a d)}-\frac{a \log \left (a+b x^3\right )}{3 b (b c-a d)} \]
[Out]
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Rubi [A] time = 0.144342, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{c \log \left (c+d x^3\right )}{3 d (b c-a d)}-\frac{a \log \left (a+b x^3\right )}{3 b (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[x^5/((a + b*x^3)*(c + d*x^3)),x]
[Out]
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Rubi in Sympy [A] time = 18.2898, size = 39, normalized size = 0.74 \[ \frac{a \log{\left (a + b x^{3} \right )}}{3 b \left (a d - b c\right )} - \frac{c \log{\left (c + d x^{3} \right )}}{3 d \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a)/(d*x**3+c),x)
[Out]
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Mathematica [A] time = 0.03819, size = 43, normalized size = 0.81 \[ -\frac{a d \log \left (a+b x^3\right )-b c \log \left (c+d x^3\right )}{3 b^2 c d-3 a b d^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/((a + b*x^3)*(c + d*x^3)),x]
[Out]
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Maple [A] time = 0.009, size = 50, normalized size = 0.9 \[{\frac{a\ln \left ( b{x}^{3}+a \right ) }{ \left ( 3\,ad-3\,bc \right ) b}}-{\frac{c\ln \left ( d{x}^{3}+c \right ) }{ \left ( 3\,ad-3\,bc \right ) d}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a)/(d*x^3+c),x)
[Out]
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Maxima [A] time = 1.37486, size = 66, normalized size = 1.25 \[ -\frac{a \log \left (b x^{3} + a\right )}{3 \,{\left (b^{2} c - a b d\right )}} + \frac{c \log \left (d x^{3} + c\right )}{3 \,{\left (b c d - a d^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/((b*x^3 + a)*(d*x^3 + c)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.285619, size = 57, normalized size = 1.08 \[ -\frac{a d \log \left (b x^{3} + a\right ) - b c \log \left (d x^{3} + c\right )}{3 \,{\left (b^{2} c d - a b d^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/((b*x^3 + a)*(d*x^3 + c)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.4572, size = 144, normalized size = 2.72 \[ \frac{a \log{\left (x^{3} + \frac{\frac{a^{3} d^{2}}{b \left (a d - b c\right )} - \frac{2 a^{2} c d}{a d - b c} + \frac{a b c^{2}}{a d - b c} + 2 a c}{a d + b c} \right )}}{3 b \left (a d - b c\right )} - \frac{c \log{\left (x^{3} + \frac{- \frac{a^{2} c d}{a d - b c} + \frac{2 a b c^{2}}{a d - b c} + 2 a c - \frac{b^{2} c^{3}}{d \left (a d - b c\right )}}{a d + b c} \right )}}{3 d \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a)/(d*x**3+c),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/((b*x^3 + a)*(d*x^3 + c)),x, algorithm="giac")
[Out]