Optimal. Leaf size=38 \[ -\frac{\log \left (a x^3+b\right )}{3 b^2}+\frac{1}{3 b \left (a x^3+b\right )}+\frac{\log (x)}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0764279, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{\log \left (a x^3+b\right )}{3 b^2}+\frac{1}{3 b \left (a x^3+b\right )}+\frac{\log (x)}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^3)^2*x^7),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.6625, size = 34, normalized size = 0.89 \[ \frac{1}{3 b \left (a x^{3} + b\right )} + \frac{\log{\left (x^{3} \right )}}{3 b^{2}} - \frac{\log{\left (a x^{3} + b \right )}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**3)**2/x**7,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0216033, size = 33, normalized size = 0.87 \[ \frac{\frac{b}{a x^3+b}-\log \left (a x^3+b\right )+3 \log (x)}{3 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^3)^2*x^7),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.011, size = 35, normalized size = 0.9 \[{\frac{1}{3\,b \left ( a{x}^{3}+b \right ) }}+{\frac{\ln \left ( x \right ) }{{b}^{2}}}-{\frac{\ln \left ( a{x}^{3}+b \right ) }{3\,{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^3)^2/x^7,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4412, size = 50, normalized size = 1.32 \[ \frac{1}{3 \,{\left (a b x^{3} + b^{2}\right )}} - \frac{\log \left (a x^{3} + b\right )}{3 \, b^{2}} + \frac{\log \left (x^{3}\right )}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^7),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.235612, size = 63, normalized size = 1.66 \[ -\frac{{\left (a x^{3} + b\right )} \log \left (a x^{3} + b\right ) - 3 \,{\left (a x^{3} + b\right )} \log \left (x\right ) - b}{3 \,{\left (a b^{2} x^{3} + b^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^7),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.9393, size = 34, normalized size = 0.89 \[ \frac{1}{3 a b x^{3} + 3 b^{2}} + \frac{\log{\left (x \right )}}{b^{2}} - \frac{\log{\left (x^{3} + \frac{b}{a} \right )}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**3)**2/x**7,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.226547, size = 61, normalized size = 1.61 \[ -\frac{{\rm ln}\left ({\left | a x^{3} + b \right |}\right )}{3 \, b^{2}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{b^{2}} + \frac{a x^{3} + 2 \, b}{3 \,{\left (a x^{3} + b\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^7),x, algorithm="giac")
[Out]