Optimal. Leaf size=44 \[ -3 b^3 \log \left (\frac{b}{\sqrt [3]{x}}+1\right )-b^3 \log (x)+3 b^2 \sqrt [3]{x}-\frac{3}{2} b x^{2/3}+x \]
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Rubi [A] time = 0.0595172, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -3 b^3 \log \left (\frac{b}{\sqrt [3]{x}}+1\right )-b^3 \log (x)+3 b^2 \sqrt [3]{x}-\frac{3}{2} b x^{2/3}+x \]
Antiderivative was successfully verified.
[In] Int[(1 + b/x^(1/3))^(-1),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 3 b^{3} \log{\left (b + \sqrt [3]{x} \right )} - 3 b \int ^{\sqrt [3]{x}} x\, dx + x + 3 \int ^{\sqrt [3]{x}} b^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+b/x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0127456, size = 35, normalized size = 0.8 \[ -3 b^3 \log \left (b+\sqrt [3]{x}\right )+3 b^2 \sqrt [3]{x}-\frac{3}{2} b x^{2/3}+x \]
Antiderivative was successfully verified.
[In] Integrate[(1 + b/x^(1/3))^(-1),x]
[Out]
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Maple [A] time = 0.005, size = 28, normalized size = 0.6 \[ x-{\frac{3\,b}{2}{x}^{{\frac{2}{3}}}}+3\,{b}^{2}\sqrt [3]{x}-3\,{b}^{3}\ln \left ( \sqrt [3]{x}+b \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+b/x^(1/3)),x)
[Out]
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Maxima [A] time = 1.48262, size = 54, normalized size = 1.23 \[ -b^{3} \log \left (x\right ) - 3 \, b^{3} \log \left (\frac{b}{x^{\frac{1}{3}}} + 1\right ) + \frac{1}{2} \,{\left (\frac{6 \, b^{2}}{x^{\frac{2}{3}}} - \frac{3 \, b}{x^{\frac{1}{3}}} + 2\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x^(1/3) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22868, size = 36, normalized size = 0.82 \[ -3 \, b^{3} \log \left (b + x^{\frac{1}{3}}\right ) + 3 \, b^{2} x^{\frac{1}{3}} - \frac{3}{2} \, b x^{\frac{2}{3}} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x^(1/3) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.407957, size = 34, normalized size = 0.77 \[ - 3 b^{3} \log{\left (b + \sqrt [3]{x} \right )} + 3 b^{2} \sqrt [3]{x} - \frac{3 b x^{\frac{2}{3}}}{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+b/x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.213372, size = 38, normalized size = 0.86 \[ -3 \, b^{3}{\rm ln}\left ({\left | b + x^{\frac{1}{3}} \right |}\right ) + 3 \, b^{2} x^{\frac{1}{3}} - \frac{3}{2} \, b x^{\frac{2}{3}} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x^(1/3) + 1),x, algorithm="giac")
[Out]