Optimal. Leaf size=69 \[ -\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3} \]
[Out]
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Rubi [A] time = 0.0793353, antiderivative size = 69, 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 \[ -\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(a + b*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 12.725, size = 66, normalized size = 0.96 \[ - \frac{1}{3 a^{2} x^{3}} + \frac{b}{a^{3} x^{2}} - \frac{b^{3}}{a^{4} \left (a + b x\right )} - \frac{3 b^{2}}{a^{4} x} - \frac{4 b^{3} \log{\left (x \right )}}{a^{5}} + \frac{4 b^{3} \log{\left (a + b x \right )}}{a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.0893661, size = 66, normalized size = 0.96 \[ -\frac{\frac{a \left (a^3-2 a^2 b x+6 a b^2 x^2+12 b^3 x^3\right )}{x^3 (a+b x)}-12 b^3 \log (a+b x)+12 b^3 \log (x)}{3 a^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(a + b*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 68, normalized size = 1. \[ -{\frac{1}{3\,{a}^{2}{x}^{3}}}+{\frac{b}{{a}^{3}{x}^{2}}}-3\,{\frac{{b}^{2}}{{a}^{4}x}}-{\frac{{b}^{3}}{{a}^{4} \left ( bx+a \right ) }}-4\,{\frac{{b}^{3}\ln \left ( x \right ) }{{a}^{5}}}+4\,{\frac{{b}^{3}\ln \left ( bx+a \right ) }{{a}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.37126, size = 99, normalized size = 1.43 \[ -\frac{12 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} - 2 \, a^{2} b x + a^{3}}{3 \,{\left (a^{4} b x^{4} + a^{5} x^{3}\right )}} + \frac{4 \, b^{3} \log \left (b x + a\right )}{a^{5}} - \frac{4 \, b^{3} \log \left (x\right )}{a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^2*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208677, size = 128, normalized size = 1.86 \[ -\frac{12 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} - 2 \, a^{3} b x + a^{4} - 12 \,{\left (b^{4} x^{4} + a b^{3} x^{3}\right )} \log \left (b x + a\right ) + 12 \,{\left (b^{4} x^{4} + a b^{3} x^{3}\right )} \log \left (x\right )}{3 \,{\left (a^{5} b x^{4} + a^{6} x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^2*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.84959, size = 66, normalized size = 0.96 \[ - \frac{a^{3} - 2 a^{2} b x + 6 a b^{2} x^{2} + 12 b^{3} x^{3}}{3 a^{5} x^{3} + 3 a^{4} b x^{4}} + \frac{4 b^{3} \left (- \log{\left (x \right )} + \log{\left (\frac{a}{b} + x \right )}\right )}{a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.231857, size = 122, normalized size = 1.77 \[ -\frac{4 \, b^{3}{\rm ln}\left ({\left | -\frac{a}{b x + a} + 1 \right |}\right )}{a^{5}} - \frac{b^{3}}{{\left (b x + a\right )} a^{4}} - \frac{\frac{30 \, a b^{3}}{b x + a} - \frac{18 \, a^{2} b^{3}}{{\left (b x + a\right )}^{2}} - 13 \, b^{3}}{3 \, a^{5}{\left (\frac{a}{b x + a} - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^2*x^4),x, algorithm="giac")
[Out]