Optimal. Leaf size=52 \[ \frac{6 a \log \left (a \sqrt [3]{x}+b\right )}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{3 a}{b^2 \left (a \sqrt [3]{x}+b\right )}-\frac{3}{b^2 \sqrt [3]{x}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0882315, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{6 a \log \left (a \sqrt [3]{x}+b\right )}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{3 a}{b^2 \left (a \sqrt [3]{x}+b\right )}-\frac{3}{b^2 \sqrt [3]{x}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^(1/3))^2*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.0973, size = 54, normalized size = 1.04 \[ - \frac{3 a}{b^{2} \left (a \sqrt [3]{x} + b\right )} - \frac{6 a \log{\left (\sqrt [3]{x} \right )}}{b^{3}} + \frac{6 a \log{\left (a \sqrt [3]{x} + b \right )}}{b^{3}} - \frac{3}{b^{2} \sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**(1/3))**2/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.101208, size = 49, normalized size = 0.94 \[ \frac{3 \left (-\frac{a b}{a \sqrt [3]{x}+b}+2 a \log \left (a \sqrt [3]{x}+b\right )-\frac{2}{3} a \log (x)-\frac{b}{\sqrt [3]{x}}\right )}{b^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^(1/3))^2*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.016, size = 47, normalized size = 0.9 \[ -3\,{\frac{a}{{b}^{2} \left ( b+a\sqrt [3]{x} \right ) }}-3\,{\frac{1}{{b}^{2}\sqrt [3]{x}}}+6\,{\frac{a\ln \left ( b+a\sqrt [3]{x} \right ) }{{b}^{3}}}-2\,{\frac{a\ln \left ( x \right ) }{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^(1/3))^2/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43214, size = 59, normalized size = 1.13 \[ \frac{6 \, a \log \left (a + \frac{b}{x^{\frac{1}{3}}}\right )}{b^{3}} - \frac{3 \,{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )}}{b^{3}} + \frac{3 \, a^{2}}{{\left (a + \frac{b}{x^{\frac{1}{3}}}\right )} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.237582, size = 101, normalized size = 1.94 \[ -\frac{3 \,{\left (2 \, a b x^{\frac{1}{3}} + b^{2} - 2 \,{\left (a^{2} x^{\frac{2}{3}} + a b x^{\frac{1}{3}}\right )} \log \left (a x^{\frac{1}{3}} + b\right ) + 2 \,{\left (a^{2} x^{\frac{2}{3}} + a b x^{\frac{1}{3}}\right )} \log \left (x^{\frac{1}{3}}\right )\right )}}{a b^{3} x^{\frac{2}{3}} + b^{4} x^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 10.258, size = 211, normalized size = 4.06 \[ \begin{cases} \frac{\tilde{\infty }}{\sqrt [3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{b^{2} \sqrt [3]{x}} & \text{for}\: a = 0 \\- \frac{1}{a^{2} x} & \text{for}\: b = 0 \\- \frac{2 a^{2} x^{2} \log{\left (x \right )}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} + \frac{6 a^{2} x^{2} \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{2 a b x^{\frac{5}{3}} \log{\left (x \right )}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} + \frac{6 a b x^{\frac{5}{3}} \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{6 a b x^{\frac{5}{3}}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} - \frac{3 b^{2} x^{\frac{4}{3}}}{a b^{3} x^{2} + b^{4} x^{\frac{5}{3}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**(1/3))**2/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.222346, size = 69, normalized size = 1.33 \[ \frac{6 \, a{\rm ln}\left ({\left | a x^{\frac{1}{3}} + b \right |}\right )}{b^{3}} - \frac{2 \, a{\rm ln}\left ({\left | x \right |}\right )}{b^{3}} - \frac{3 \,{\left (2 \, a x^{\frac{1}{3}} + b\right )}}{{\left (a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x^2),x, algorithm="giac")
[Out]