Optimal. Leaf size=36 \[ \frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d} \]
[Out]
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Rubi [A] time = 0.0259394, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\log (a+b x)}{b c-a d}-\frac{\log (c+d x)}{b c-a d} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)*(c + d*x)),x]
[Out]
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Rubi in Sympy [A] time = 5.66021, size = 26, normalized size = 0.72 \[ - \frac{\log{\left (a + b x \right )}}{a d - b c} + \frac{\log{\left (c + d x \right )}}{a d - b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)/(d*x+c),x)
[Out]
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Mathematica [A] time = 0.0178339, size = 26, normalized size = 0.72 \[ \frac{\log (a+b x)-\log (c+d x)}{b c-a d} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)*(c + d*x)),x]
[Out]
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Maple [A] time = 0.008, size = 37, normalized size = 1. \[{\frac{\ln \left ( dx+c \right ) }{ad-bc}}-{\frac{\ln \left ( bx+a \right ) }{ad-bc}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)/(d*x+c),x)
[Out]
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Maxima [A] time = 1.34593, size = 49, normalized size = 1.36 \[ \frac{\log \left (b x + a\right )}{b c - a d} - \frac{\log \left (d x + c\right )}{b c - a d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + c)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207315, size = 35, normalized size = 0.97 \[ \frac{\log \left (b x + a\right ) - \log \left (d x + c\right )}{b c - a d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*(d*x + c)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.46207, size = 128, normalized size = 3.56 \[ \frac{\log{\left (x + \frac{- \frac{a^{2} d^{2}}{a d - b c} + \frac{2 a b c d}{a d - b c} + a d - \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right )}}{a d - b c} - \frac{\log{\left (x + \frac{\frac{a^{2} d^{2}}{a d - b c} - \frac{2 a b c d}{a d - b c} + a d + \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right )}}{a d - b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)/(d*x+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(1/((b*x + a)*(d*x + c)),x, algorithm="giac")
[Out]