Optimal. Leaf size=42 \[ \frac{a^2 \log (x)}{b^3}-\frac{a^2 \log (a x+b)}{b^3}+\frac{a}{b^2 x}-\frac{1}{2 b x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0552284, 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 \[ \frac{a^2 \log (x)}{b^3}-\frac{a^2 \log (a x+b)}{b^3}+\frac{a}{b^2 x}-\frac{1}{2 b x^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.39716, size = 37, normalized size = 0.88 \[ \frac{a^{2} \log{\left (x \right )}}{b^{3}} - \frac{a^{2} \log{\left (a x + b \right )}}{b^{3}} + \frac{a}{b^{2} x} - \frac{1}{2 b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)/x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00818869, size = 42, normalized size = 1. \[ \frac{a^2 \log (x)}{b^3}-\frac{a^2 \log (a x+b)}{b^3}+\frac{a}{b^2 x}-\frac{1}{2 b x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.013, size = 41, normalized size = 1. \[ -{\frac{1}{2\,b{x}^{2}}}+{\frac{a}{{b}^{2}x}}+{\frac{{a}^{2}\ln \left ( x \right ) }{{b}^{3}}}-{\frac{{a}^{2}\ln \left ( ax+b \right ) }{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)/x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43762, size = 54, normalized size = 1.29 \[ -\frac{a^{2} \log \left (a x + b\right )}{b^{3}} + \frac{a^{2} \log \left (x\right )}{b^{3}} + \frac{2 \, a x - b}{2 \, b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226613, size = 55, normalized size = 1.31 \[ -\frac{2 \, a^{2} x^{2} \log \left (a x + b\right ) - 2 \, a^{2} x^{2} \log \left (x\right ) - 2 \, a b x + b^{2}}{2 \, b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.39915, size = 31, normalized size = 0.74 \[ \frac{a^{2} \left (\log{\left (x \right )} - \log{\left (x + \frac{b}{a} \right )}\right )}{b^{3}} + \frac{2 a x - b}{2 b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)/x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223123, size = 61, normalized size = 1.45 \[ -\frac{a^{2}{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{3}} + \frac{a^{2}{\rm ln}\left ({\left | x \right |}\right )}{b^{3}} + \frac{2 \, a b x - b^{2}}{2 \, b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^4),x, algorithm="giac")
[Out]