Optimal. Leaf size=42 \[ -\frac{2 a \log (x)}{b^3}+\frac{2 a \log (a x+b)}{b^3}-\frac{a}{b^2 (a x+b)}-\frac{1}{b^2 x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0678242, antiderivative size = 42, 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 \[ -\frac{2 a \log (x)}{b^3}+\frac{2 a \log (a x+b)}{b^3}-\frac{a}{b^2 (a x+b)}-\frac{1}{b^2 x} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^2*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.74181, size = 39, normalized size = 0.93 \[ - \frac{a}{b^{2} \left (a x + b\right )} - \frac{2 a \log{\left (x \right )}}{b^{3}} + \frac{2 a \log{\left (a x + b \right )}}{b^{3}} - \frac{1}{b^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**2/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0705966, size = 35, normalized size = 0.83 \[ -\frac{b \left (\frac{a}{a x+b}+\frac{1}{x}\right )-2 a \log (a x+b)+2 a \log (x)}{b^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^2*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.015, size = 43, normalized size = 1. \[ -{\frac{1}{{b}^{2}x}}-{\frac{a}{{b}^{2} \left ( ax+b \right ) }}-2\,{\frac{a\ln \left ( x \right ) }{{b}^{3}}}+2\,{\frac{a\ln \left ( ax+b \right ) }{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^2/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.45739, size = 61, normalized size = 1.45 \[ -\frac{2 \, a x + b}{a b^{2} x^{2} + b^{3} x} + \frac{2 \, a \log \left (a x + b\right )}{b^{3}} - \frac{2 \, a \log \left (x\right )}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221001, size = 85, normalized size = 2.02 \[ -\frac{2 \, a b x + b^{2} - 2 \,{\left (a^{2} x^{2} + a b x\right )} \log \left (a x + b\right ) + 2 \,{\left (a^{2} x^{2} + a b x\right )} \log \left (x\right )}{a b^{3} x^{2} + b^{4} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.5943, size = 36, normalized size = 0.86 \[ \frac{2 a \left (- \log{\left (x \right )} + \log{\left (x + \frac{b}{a} \right )}\right )}{b^{3}} - \frac{2 a x + b}{a b^{2} x^{2} + b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**2/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.229185, size = 61, normalized size = 1.45 \[ \frac{2 \, a{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{3}} - \frac{2 \, a{\rm ln}\left ({\left | x \right |}\right )}{b^{3}} - \frac{2 \, a x + b}{{\left (a x^{2} + b x\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^4),x, algorithm="giac")
[Out]