Optimal. Leaf size=35 \[ -\frac{b \log \left (a-b x^2\right )}{2 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2} \]
[Out]
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Rubi [A] time = 0.0606195, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{b \log \left (a-b x^2\right )}{2 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(a - b*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 9.48546, size = 34, normalized size = 0.97 \[ - \frac{1}{2 a x^{2}} + \frac{b \log{\left (x^{2} \right )}}{2 a^{2}} - \frac{b \log{\left (a - b x^{2} \right )}}{2 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(-b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.0142872, size = 35, normalized size = 1. \[ -\frac{b \log \left (a-b x^2\right )}{2 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(a - b*x^2)),x]
[Out]
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Maple [A] time = 0.008, size = 33, normalized size = 0.9 \[ -{\frac{1}{2\,a{x}^{2}}}+{\frac{b\ln \left ( x \right ) }{{a}^{2}}}-{\frac{b\ln \left ( b{x}^{2}-a \right ) }{2\,{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(-b*x^2+a),x)
[Out]
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Maxima [A] time = 1.35136, size = 47, normalized size = 1.34 \[ -\frac{b \log \left (b x^{2} - a\right )}{2 \, a^{2}} + \frac{b \log \left (x^{2}\right )}{2 \, a^{2}} - \frac{1}{2 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206204, size = 45, normalized size = 1.29 \[ -\frac{b x^{2} \log \left (b x^{2} - a\right ) - 2 \, b x^{2} \log \left (x\right ) + a}{2 \, a^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.65492, size = 31, normalized size = 0.89 \[ - \frac{1}{2 a x^{2}} + \frac{b \log{\left (x \right )}}{a^{2}} - \frac{b \log{\left (- \frac{a}{b} + x^{2} \right )}}{2 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(-b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.211988, size = 58, normalized size = 1.66 \[ \frac{b{\rm ln}\left (x^{2}\right )}{2 \, a^{2}} - \frac{b{\rm ln}\left ({\left | b x^{2} - a \right |}\right )}{2 \, a^{2}} - \frac{b x^{2} + a}{2 \, a^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((b*x^2 - a)*x^3),x, algorithm="giac")
[Out]