Optimal. Leaf size=68 \[ \frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b^3}{a^4 x}-\frac{b^2}{2 a^3 x^2}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4} \]
[Out]
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Rubi [A] time = 0.0584225, antiderivative size = 68, 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 \[ \frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b^3}{a^4 x}-\frac{b^2}{2 a^3 x^2}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4} \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 11.0919, size = 61, normalized size = 0.9 \[ - \frac{1}{4 a x^{4}} + \frac{b}{3 a^{2} x^{3}} - \frac{b^{2}}{2 a^{3} x^{2}} + \frac{b^{3}}{a^{4} x} + \frac{b^{4} \log{\left (x \right )}}{a^{5}} - \frac{b^{4} \log{\left (a + b x \right )}}{a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00676188, size = 68, normalized size = 1. \[ \frac{b^4 \log (x)}{a^5}-\frac{b^4 \log (a+b x)}{a^5}+\frac{b^3}{a^4 x}-\frac{b^2}{2 a^3 x^2}+\frac{b}{3 a^2 x^3}-\frac{1}{4 a x^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(a + b*x)),x]
[Out]
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Maple [A] time = 0.013, size = 63, normalized size = 0.9 \[ -{\frac{1}{4\,a{x}^{4}}}+{\frac{b}{3\,{a}^{2}{x}^{3}}}-{\frac{{b}^{2}}{2\,{a}^{3}{x}^{2}}}+{\frac{{b}^{3}}{{a}^{4}x}}+{\frac{{b}^{4}\ln \left ( x \right ) }{{a}^{5}}}-{\frac{{b}^{4}\ln \left ( bx+a \right ) }{{a}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(b*x+a),x)
[Out]
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Maxima [A] time = 1.34621, size = 84, normalized size = 1.24 \[ -\frac{b^{4} \log \left (b x + a\right )}{a^{5}} + \frac{b^{4} \log \left (x\right )}{a^{5}} + \frac{12 \, b^{3} x^{3} - 6 \, a b^{2} x^{2} + 4 \, a^{2} b x - 3 \, a^{3}}{12 \, a^{4} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200885, size = 88, normalized size = 1.29 \[ -\frac{12 \, b^{4} x^{4} \log \left (b x + a\right ) - 12 \, b^{4} x^{4} \log \left (x\right ) - 12 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} - 4 \, a^{3} b x + 3 \, a^{4}}{12 \, a^{5} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.59872, size = 56, normalized size = 0.82 \[ \frac{- 3 a^{3} + 4 a^{2} b x - 6 a b^{2} x^{2} + 12 b^{3} x^{3}}{12 a^{4} x^{4}} + \frac{b^{4} \left (\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}\right )}{a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.218773, size = 90, normalized size = 1.32 \[ -\frac{b^{4}{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{5}} + \frac{b^{4}{\rm ln}\left ({\left | x \right |}\right )}{a^{5}} + \frac{12 \, a b^{3} x^{3} - 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x - 3 \, a^{4}}{12 \, a^{5} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)*x^5),x, algorithm="giac")
[Out]