Optimal. Leaf size=16 \[ \frac{x \left (a+\frac{b}{\sqrt [3]{x}}\right )^3}{a} \]
[Out]
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Rubi [A] time = 0.0252124, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x \left (a+\frac{b}{\sqrt [3]{x}}\right )^3}{a} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^2,x]
[Out]
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Rubi in Sympy [A] time = 1.28571, size = 12, normalized size = 0.75 \[ \frac{x \left (a + \frac{b}{\sqrt [3]{x}}\right )^{3}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**2,x)
[Out]
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Mathematica [A] time = 0.007462, size = 25, normalized size = 1.56 \[ a^2 x+3 a b x^{2/3}+3 b^2 \sqrt [3]{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^2,x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \[{\frac{1}{a} \left ( b+a\sqrt [3]{x} \right ) ^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^2,x)
[Out]
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Maxima [A] time = 1.441, size = 28, normalized size = 1.75 \[ a^{2} x + 3 \, a b x^{\frac{2}{3}} + 3 \, b^{2} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217698, size = 28, normalized size = 1.75 \[ a^{2} x + 3 \, a b x^{\frac{2}{3}} + 3 \, b^{2} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.421584, size = 24, normalized size = 1.5 \[ a^{2} x + 3 a b x^{\frac{2}{3}} + 3 b^{2} \sqrt [3]{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211036, size = 28, normalized size = 1.75 \[ a^{2} x + 3 \, a b x^{\frac{2}{3}} + 3 \, b^{2} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^2,x, algorithm="giac")
[Out]