Optimal. Leaf size=25 \[ \frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b} \]
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Rubi [A] time = 0.0380137, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)/(a + b*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int B\, dx}{b} + \frac{\left (A b - B a\right ) \log{\left (a + b x \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.0125523, size = 25, normalized size = 1. \[ \frac{(A b-a B) \log (a+b x)}{b^2}+\frac{B x}{b} \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)/(a + b*x),x]
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Maple [A] time = 0.002, size = 32, normalized size = 1.3 \[{\frac{Bx}{b}}+{\frac{\ln \left ( bx+a \right ) A}{b}}-{\frac{\ln \left ( bx+a \right ) Ba}{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)/(b*x+a),x)
[Out]
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Maxima [A] time = 1.3442, size = 35, normalized size = 1.4 \[ \frac{B x}{b} - \frac{{\left (B a - A b\right )} \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b*x + a),x, algorithm="maxima")
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Fricas [A] time = 0.213457, size = 34, normalized size = 1.36 \[ \frac{B b x -{\left (B a - A b\right )} \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.23174, size = 20, normalized size = 0.8 \[ \frac{B x}{b} - \frac{\left (- A b + B a\right ) \log{\left (a + b x \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.22582, size = 36, normalized size = 1.44 \[ \frac{B x}{b} - \frac{{\left (B a - A b\right )}{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b*x + a),x, algorithm="giac")
[Out]