Optimal. Leaf size=104 \[ -\frac{3 b^6 \log \left (a+b \sqrt [3]{x}\right )}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{3 b^5}{a^6 \sqrt [3]{x}}-\frac{3 b^4}{2 a^5 x^{2/3}}+\frac{b^3}{a^4 x}-\frac{3 b^2}{4 a^3 x^{4/3}}+\frac{3 b}{5 a^2 x^{5/3}}-\frac{1}{2 a x^2} \]
[Out]
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Rubi [A] time = 0.128783, antiderivative size = 104, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{3 b^6 \log \left (a+b \sqrt [3]{x}\right )}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{3 b^5}{a^6 \sqrt [3]{x}}-\frac{3 b^4}{2 a^5 x^{2/3}}+\frac{b^3}{a^4 x}-\frac{3 b^2}{4 a^3 x^{4/3}}+\frac{3 b}{5 a^2 x^{5/3}}-\frac{1}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x^(1/3))*x^3),x]
[Out]
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Rubi in Sympy [A] time = 20.2577, size = 107, normalized size = 1.03 \[ - \frac{1}{2 a x^{2}} + \frac{3 b}{5 a^{2} x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 a^{3} x^{\frac{4}{3}}} + \frac{b^{3}}{a^{4} x} - \frac{3 b^{4}}{2 a^{5} x^{\frac{2}{3}}} + \frac{3 b^{5}}{a^{6} \sqrt [3]{x}} + \frac{3 b^{6} \log{\left (\sqrt [3]{x} \right )}}{a^{7}} - \frac{3 b^{6} \log{\left (a + b \sqrt [3]{x} \right )}}{a^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*x**(1/3))/x**3,x)
[Out]
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Mathematica [A] time = 0.0699572, size = 95, normalized size = 0.91 \[ \frac{\frac{a \left (-10 a^5+12 a^4 b \sqrt [3]{x}-15 a^3 b^2 x^{2/3}+20 a^2 b^3 x-30 a b^4 x^{4/3}+60 b^5 x^{5/3}\right )}{x^2}-60 b^6 \log \left (a+b \sqrt [3]{x}\right )+20 b^6 \log (x)}{20 a^7} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x^(1/3))*x^3),x]
[Out]
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Maple [A] time = 0.003, size = 87, normalized size = 0.8 \[ -{\frac{1}{2\,a{x}^{2}}}+{\frac{3\,b}{5\,{a}^{2}}{x}^{-{\frac{5}{3}}}}-{\frac{3\,{b}^{2}}{4\,{a}^{3}}{x}^{-{\frac{4}{3}}}}+{\frac{{b}^{3}}{{a}^{4}x}}-{\frac{3\,{b}^{4}}{2\,{a}^{5}}{x}^{-{\frac{2}{3}}}}+3\,{\frac{{b}^{5}}{{a}^{6}\sqrt [3]{x}}}-3\,{\frac{{b}^{6}\ln \left ( a+b\sqrt [3]{x} \right ) }{{a}^{7}}}+{\frac{{b}^{6}\ln \left ( x \right ) }{{a}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b*x^(1/3))/x^3,x)
[Out]
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Maxima [A] time = 1.4387, size = 116, normalized size = 1.12 \[ -\frac{3 \, b^{6} \log \left (b x^{\frac{1}{3}} + a\right )}{a^{7}} + \frac{b^{6} \log \left (x\right )}{a^{7}} + \frac{60 \, b^{5} x^{\frac{5}{3}} - 30 \, a b^{4} x^{\frac{4}{3}} + 20 \, a^{2} b^{3} x - 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 12 \, a^{4} b x^{\frac{1}{3}} - 10 \, a^{5}}{20 \, a^{6} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226224, size = 126, normalized size = 1.21 \[ -\frac{60 \, b^{6} x^{2} \log \left (b x^{\frac{1}{3}} + a\right ) - 60 \, b^{6} x^{2} \log \left (x^{\frac{1}{3}}\right ) - 20 \, a^{3} b^{3} x + 10 \, a^{6} - 15 \,{\left (4 \, a b^{5} x - a^{4} b^{2}\right )} x^{\frac{2}{3}} + 6 \,{\left (5 \, a^{2} b^{4} x - 2 \, a^{5} b\right )} x^{\frac{1}{3}}}{20 \, a^{7} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 30.4538, size = 129, normalized size = 1.24 \[ \begin{cases} \frac{\tilde{\infty }}{x^{\frac{7}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{7 b x^{\frac{7}{3}}} & \text{for}\: a = 0 \\- \frac{1}{2 a x^{2}} & \text{for}\: b = 0 \\- \frac{1}{2 a x^{2}} + \frac{3 b}{5 a^{2} x^{\frac{5}{3}}} - \frac{3 b^{2}}{4 a^{3} x^{\frac{4}{3}}} + \frac{b^{3}}{a^{4} x} - \frac{3 b^{4}}{2 a^{5} x^{\frac{2}{3}}} + \frac{3 b^{5}}{a^{6} \sqrt [3]{x}} + \frac{b^{6} \log{\left (x \right )}}{a^{7}} - \frac{3 b^{6} \log{\left (\frac{a}{b} + \sqrt [3]{x} \right )}}{a^{7}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b*x**(1/3))/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.222569, size = 123, normalized size = 1.18 \[ -\frac{3 \, b^{6}{\rm ln}\left ({\left | b x^{\frac{1}{3}} + a \right |}\right )}{a^{7}} + \frac{b^{6}{\rm ln}\left ({\left | x \right |}\right )}{a^{7}} + \frac{60 \, a b^{5} x^{\frac{5}{3}} - 30 \, a^{2} b^{4} x^{\frac{4}{3}} + 20 \, a^{3} b^{3} x - 15 \, a^{4} b^{2} x^{\frac{2}{3}} + 12 \, a^{5} b x^{\frac{1}{3}} - 10 \, a^{6}}{20 \, a^{7} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^(1/3) + a)*x^3),x, algorithm="giac")
[Out]