Optimal. Leaf size=86 \[ \frac{b \log (a+b x)}{(b c-a d) (b e-a f)}-\frac{d \log (c+d x)}{(b c-a d) (d e-c f)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)} \]
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Rubi [A] time = 0.161118, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{b \log (a+b x)}{(b c-a d) (b e-a f)}-\frac{d \log (c+d x)}{(b c-a d) (d e-c f)}+\frac{f \log (e+f x)}{(b e-a f) (d e-c f)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)*(c + d*x)*(e + f*x)),x]
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Rubi in Sympy [A] time = 25.0541, size = 65, normalized size = 0.76 \[ \frac{b \log{\left (a + b x \right )}}{\left (a d - b c\right ) \left (a f - b e\right )} - \frac{d \log{\left (c + d x \right )}}{\left (a d - b c\right ) \left (c f - d e\right )} + \frac{f \log{\left (e + f x \right )}}{\left (a f - b e\right ) \left (c f - d e\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)/(d*x+c)/(f*x+e),x)
[Out]
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Mathematica [A] time = 0.0852806, size = 80, normalized size = 0.93 \[ \frac{b \log (a+b x) (c f-d e)+d (b e-a f) \log (c+d x)+f (a d-b c) \log (e+f x)}{(b c-a d) (b e-a f) (c f-d e)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)*(c + d*x)*(e + f*x)),x]
[Out]
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Maple [A] time = 0.011, size = 87, normalized size = 1. \[ -{\frac{d\ln \left ( dx+c \right ) }{ \left ( ad-bc \right ) \left ( cf-de \right ) }}+{\frac{b\ln \left ( bx+a \right ) }{ \left ( ad-bc \right ) \left ( af-be \right ) }}+{\frac{f\ln \left ( fx+e \right ) }{ \left ( af-be \right ) \left ( cf-de \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)/(d*x+c)/(f*x+e),x)
[Out]
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Maxima [A] time = 1.35754, size = 151, normalized size = 1.76 \[ \frac{b \log \left (b x + a\right )}{{\left (b^{2} c - a b d\right )} e -{\left (a b c - a^{2} d\right )} f} - \frac{d \log \left (d x + c\right )}{{\left (b c d - a d^{2}\right )} e -{\left (b c^{2} - a c d\right )} f} + \frac{f \log \left (f x + e\right )}{b d e^{2} + a c f^{2} -{\left (b c + a d\right )} e f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + c)*(f*x + e)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 5.4974, size = 151, normalized size = 1.76 \[ \frac{{\left (b c - a d\right )} f \log \left (f x + e\right ) +{\left (b d e - b c f\right )} \log \left (b x + a\right ) -{\left (b d e - a d f\right )} \log \left (d x + c\right )}{{\left (b^{2} c d - a b d^{2}\right )} e^{2} -{\left (b^{2} c^{2} - a^{2} d^{2}\right )} e f +{\left (a b c^{2} - a^{2} c d\right )} f^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + c)*(f*x + e)),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)/(d*x+c)/(f*x+e),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}{\left (d x + c\right )}{\left (f x + e\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + c)*(f*x + e)),x, algorithm="giac")
[Out]