Optimal. Leaf size=40 \[ \frac{(a p+b) \log (p-x)}{p-q}-\frac{(a q+b) \log (q-x)}{p-q} \]
[Out]
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Rubi [A] time = 0.0637384, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{(a p+b) \log (p-x)}{p-q}-\frac{(a q+b) \log (q-x)}{p-q} \]
Antiderivative was successfully verified.
[In] Int[(b + a*x)/((-p + x)*(-q + x)),x]
[Out]
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Rubi in Sympy [A] time = 4.94215, size = 26, normalized size = 0.65 \[ \frac{\left (a p + b\right ) \log{\left (p - x \right )}}{p - q} - \frac{\left (a q + b\right ) \log{\left (q - x \right )}}{p - q} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*x+b)/(-p+x)/(-q+x),x)
[Out]
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Mathematica [A] time = 0.0225985, size = 34, normalized size = 0.85 \[ \frac{(a p+b) \log (x-p)-(a q+b) \log (x-q)}{p-q} \]
Antiderivative was successfully verified.
[In] Integrate[(b + a*x)/((-p + x)*(-q + x)),x]
[Out]
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Maple [A] time = 0.005, size = 66, normalized size = 1.7 \[{\frac{\ln \left ( -p+x \right ) ap}{p-q}}+{\frac{\ln \left ( -p+x \right ) b}{p-q}}-{\frac{\ln \left ( -q+x \right ) aq}{p-q}}-{\frac{\ln \left ( -q+x \right ) b}{p-q}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*x+b)/(-p+x)/(-q+x),x)
[Out]
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Maxima [A] time = 1.37392, size = 54, normalized size = 1.35 \[ \frac{{\left (a p + b\right )} \log \left (-p + x\right )}{p - q} - \frac{{\left (a q + b\right )} \log \left (-q + x\right )}{p - q} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)/((p - x)*(q - x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201657, size = 46, normalized size = 1.15 \[ \frac{{\left (a p + b\right )} \log \left (-p + x\right ) -{\left (a q + b\right )} \log \left (-q + x\right )}{p - q} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)/((p - x)*(q - x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.03251, size = 144, normalized size = 3.6 \[ \frac{\left (a p + b\right ) \log{\left (x + \frac{- 2 a p q - b p - b q - \frac{p^{2} \left (a p + b\right )}{p - q} + \frac{2 p q \left (a p + b\right )}{p - q} - \frac{q^{2} \left (a p + b\right )}{p - q}}{a p + a q + 2 b} \right )}}{p - q} - \frac{\left (a q + b\right ) \log{\left (x + \frac{- 2 a p q - b p - b q + \frac{p^{2} \left (a q + b\right )}{p - q} - \frac{2 p q \left (a q + b\right )}{p - q} + \frac{q^{2} \left (a q + b\right )}{p - q}}{a p + a q + 2 b} \right )}}{p - q} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x+b)/(-p+x)/(-q+x),x)
[Out]
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GIAC/XCAS [A] time = 0.209679, size = 57, normalized size = 1.42 \[ \frac{{\left (a p + b\right )}{\rm ln}\left ({\left | -p + x \right |}\right )}{p - q} - \frac{{\left (a q + b\right )}{\rm ln}\left ({\left | -q + x \right |}\right )}{p - q} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)/((p - x)*(q - x)),x, algorithm="giac")
[Out]