Optimal. Leaf size=56 \[ -\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}-\frac{a^2}{b^3 x}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3} \]
[Out]
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Rubi [A] time = 0.0712666, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}-\frac{a^2}{b^3 x}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)*x^5),x]
[Out]
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Rubi in Sympy [A] time = 11.086, size = 49, normalized size = 0.88 \[ - \frac{a^{3} \log{\left (x \right )}}{b^{4}} + \frac{a^{3} \log{\left (a x + b \right )}}{b^{4}} - \frac{a^{2}}{b^{3} x} + \frac{a}{2 b^{2} x^{2}} - \frac{1}{3 b x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)/x**5,x)
[Out]
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Mathematica [A] time = 0.00972204, size = 56, normalized size = 1. \[ -\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}-\frac{a^2}{b^3 x}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)*x^5),x]
[Out]
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Maple [A] time = 0.011, size = 53, normalized size = 1. \[ -{\frac{1}{3\,b{x}^{3}}}+{\frac{a}{2\,{b}^{2}{x}^{2}}}-{\frac{{a}^{2}}{{b}^{3}x}}-{\frac{{a}^{3}\ln \left ( x \right ) }{{b}^{4}}}+{\frac{{a}^{3}\ln \left ( ax+b \right ) }{{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)/x^5,x)
[Out]
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Maxima [A] time = 1.41971, size = 69, normalized size = 1.23 \[ \frac{a^{3} \log \left (a x + b\right )}{b^{4}} - \frac{a^{3} \log \left (x\right )}{b^{4}} - \frac{6 \, a^{2} x^{2} - 3 \, a b x + 2 \, b^{2}}{6 \, b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227135, size = 73, normalized size = 1.3 \[ \frac{6 \, a^{3} x^{3} \log \left (a x + b\right ) - 6 \, a^{3} x^{3} \log \left (x\right ) - 6 \, a^{2} b x^{2} + 3 \, a b^{2} x - 2 \, b^{3}}{6 \, b^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.54706, size = 44, normalized size = 0.79 \[ \frac{a^{3} \left (- \log{\left (x \right )} + \log{\left (x + \frac{b}{a} \right )}\right )}{b^{4}} - \frac{6 a^{2} x^{2} - 3 a b x + 2 b^{2}}{6 b^{3} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.231316, size = 76, normalized size = 1.36 \[ \frac{a^{3}{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{4}} - \frac{a^{3}{\rm ln}\left ({\left | x \right |}\right )}{b^{4}} - \frac{6 \, a^{2} b x^{2} - 3 \, a b^{2} x + 2 \, b^{3}}{6 \, b^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^5),x, algorithm="giac")
[Out]