Optimal. Leaf size=28 \[ -\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x} \]
[Out]
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Rubi [A] time = 0.0315487, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 5.72571, size = 24, normalized size = 0.86 \[ - \frac{1}{a x} - \frac{b \log{\left (x \right )}}{a^{2}} + \frac{b \log{\left (a + b x \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00674428, size = 28, normalized size = 1. \[ -\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(a + b*x)),x]
[Out]
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Maple [A] time = 0.014, size = 29, normalized size = 1. \[ -{\frac{1}{ax}}-{\frac{b\ln \left ( x \right ) }{{a}^{2}}}+{\frac{b\ln \left ( bx+a \right ) }{{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x+a),x)
[Out]
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Maxima [A] time = 1.34077, size = 38, normalized size = 1.36 \[ \frac{b \log \left (b x + a\right )}{a^{2}} - \frac{b \log \left (x\right )}{a^{2}} - \frac{1}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199765, size = 35, normalized size = 1.25 \[ \frac{b x \log \left (b x + a\right ) - b x \log \left (x\right ) - a}{a^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.27486, size = 19, normalized size = 0.68 \[ - \frac{1}{a x} + \frac{b \left (- \log{\left (x \right )} + \log{\left (\frac{a}{b} + x \right )}\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.216976, size = 41, normalized size = 1.46 \[ \frac{b{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{2}} - \frac{b{\rm ln}\left ({\left | x \right |}\right )}{a^{2}} - \frac{1}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^2),x, algorithm="giac")
[Out]