Optimal. Leaf size=42 \[ \frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2} \]
[Out]
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Rubi [A] time = 0.0402526, antiderivative size = 42, 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 \[ \frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 7.59428, size = 37, normalized size = 0.88 \[ - \frac{1}{2 a x^{2}} + \frac{b}{a^{2} x} + \frac{b^{2} \log{\left (x \right )}}{a^{3}} - \frac{b^{2} \log{\left (a + b x \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00651453, size = 42, normalized size = 1. \[ \frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(a + b*x)),x]
[Out]
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Maple [A] time = 0.011, size = 41, normalized size = 1. \[ -{\frac{1}{2\,a{x}^{2}}}+{\frac{b}{{a}^{2}x}}+{\frac{{b}^{2}\ln \left ( x \right ) }{{a}^{3}}}-{\frac{{b}^{2}\ln \left ( bx+a \right ) }{{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(b*x+a),x)
[Out]
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Maxima [A] time = 1.34059, size = 54, normalized size = 1.29 \[ -\frac{b^{2} \log \left (b x + a\right )}{a^{3}} + \frac{b^{2} \log \left (x\right )}{a^{3}} + \frac{2 \, b x - a}{2 \, a^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199177, size = 55, normalized size = 1.31 \[ -\frac{2 \, b^{2} x^{2} \log \left (b x + a\right ) - 2 \, b^{2} x^{2} \log \left (x\right ) - 2 \, a b x + a^{2}}{2 \, a^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.40797, size = 31, normalized size = 0.74 \[ \frac{- a + 2 b x}{2 a^{2} x^{2}} + \frac{b^{2} \left (\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}\right )}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.207017, size = 61, normalized size = 1.45 \[ -\frac{b^{2}{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{3}} + \frac{b^{2}{\rm ln}\left ({\left | x \right |}\right )}{a^{3}} + \frac{2 \, a b x - a^{2}}{2 \, a^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^3),x, algorithm="giac")
[Out]