Optimal. Leaf size=18 \[ \frac{x}{b}-\frac{a \log (a+b x)}{b^2} \]
[Out]
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Rubi [A] time = 0.0215182, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{x}{b}-\frac{a \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a \log{\left (a + b x \right )}}{b^{2}} + \int \frac{1}{b}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00325391, size = 18, normalized size = 1. \[ \frac{x}{b}-\frac{a \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 1.1 \[{\frac{x}{b}}-{\frac{a\ln \left ( bx+a \right ) }{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x+a),x)
[Out]
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Maxima [A] time = 1.42164, size = 24, normalized size = 1.33 \[ \frac{x}{b} - \frac{a \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201912, size = 23, normalized size = 1.28 \[ \frac{b x - a \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.477018, size = 14, normalized size = 0.78 \[ - \frac{a \log{\left (a + b x \right )}}{b^{2}} + \frac{x}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.203463, size = 26, normalized size = 1.44 \[ \frac{x}{b} - \frac{a{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a),x, algorithm="giac")
[Out]