Optimal. Leaf size=57 \[ -\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{1}{a^3 (a+b x)}+\frac{1}{2 a^2 (a+b x)^2}+\frac{1}{3 a (a+b x)^3} \]
[Out]
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Rubi [A] time = 0.0602294, antiderivative size = 57, 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 \[ -\frac{\log (a+b x)}{a^4}+\frac{\log (x)}{a^4}+\frac{1}{a^3 (a+b x)}+\frac{1}{2 a^2 (a+b x)^2}+\frac{1}{3 a (a+b x)^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a + b*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 10.8952, size = 51, normalized size = 0.89 \[ \frac{1}{3 a \left (a + b x\right )^{3}} + \frac{1}{2 a^{2} \left (a + b x\right )^{2}} + \frac{1}{a^{3} \left (a + b x\right )} + \frac{\log{\left (x \right )}}{a^{4}} - \frac{\log{\left (a + b x \right )}}{a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x+a)**4,x)
[Out]
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Mathematica [A] time = 0.0517304, size = 48, normalized size = 0.84 \[ \frac{\frac{a \left (11 a^2+15 a b x+6 b^2 x^2\right )}{(a+b x)^3}-6 \log (a+b x)+6 \log (x)}{6 a^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a + b*x)^4),x]
[Out]
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Maple [A] time = 0.012, size = 54, normalized size = 1. \[{\frac{1}{3\,a \left ( bx+a \right ) ^{3}}}+{\frac{1}{2\,{a}^{2} \left ( bx+a \right ) ^{2}}}+{\frac{1}{{a}^{3} \left ( bx+a \right ) }}+{\frac{\ln \left ( x \right ) }{{a}^{4}}}-{\frac{\ln \left ( bx+a \right ) }{{a}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x+a)^4,x)
[Out]
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Maxima [A] time = 1.34044, size = 99, normalized size = 1.74 \[ \frac{6 \, b^{2} x^{2} + 15 \, a b x + 11 \, a^{2}}{6 \,{\left (a^{3} b^{3} x^{3} + 3 \, a^{4} b^{2} x^{2} + 3 \, a^{5} b x + a^{6}\right )}} - \frac{\log \left (b x + a\right )}{a^{4}} + \frac{\log \left (x\right )}{a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^4*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214982, size = 167, normalized size = 2.93 \[ \frac{6 \, a b^{2} x^{2} + 15 \, a^{2} b x + 11 \, a^{3} - 6 \,{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )} \log \left (b x + a\right ) + 6 \,{\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right )} \log \left (x\right )}{6 \,{\left (a^{4} b^{3} x^{3} + 3 \, a^{5} b^{2} x^{2} + 3 \, a^{6} b x + a^{7}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^4*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.98516, size = 70, normalized size = 1.23 \[ \frac{11 a^{2} + 15 a b x + 6 b^{2} x^{2}}{6 a^{6} + 18 a^{5} b x + 18 a^{4} b^{2} x^{2} + 6 a^{3} b^{3} x^{3}} + \frac{\log{\left (x \right )} - \log{\left (\frac{a}{b} + x \right )}}{a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x+a)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.203031, size = 73, normalized size = 1.28 \[ -\frac{{\rm ln}\left ({\left | b x + a \right |}\right )}{a^{4}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a^{4}} + \frac{6 \, a b^{2} x^{2} + 15 \, a^{2} b x + 11 \, a^{3}}{6 \,{\left (b x + a\right )}^{3} a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^4*x),x, algorithm="giac")
[Out]