Optimal. Leaf size=33 \[ \frac{3 b}{a^2 \left (a \sqrt [3]{x}+b\right )}+\frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a^2} \]
[Out]
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Rubi [A] time = 0.0604464, antiderivative size = 33, 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 \[ \frac{3 b}{a^2 \left (a \sqrt [3]{x}+b\right )}+\frac{3 \log \left (a \sqrt [3]{x}+b\right )}{a^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^(1/3))^2*x),x]
[Out]
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Rubi in Sympy [A] time = 9.14488, size = 29, normalized size = 0.88 \[ \frac{3 b}{a^{2} \left (a \sqrt [3]{x} + b\right )} + \frac{3 \log{\left (a \sqrt [3]{x} + b \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**(1/3))**2/x,x)
[Out]
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Mathematica [A] time = 0.0213829, size = 29, normalized size = 0.88 \[ \frac{3 \left (\frac{b}{a \sqrt [3]{x}+b}+\log \left (a \sqrt [3]{x}+b\right )\right )}{a^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^(1/3))^2*x),x]
[Out]
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Maple [A] time = 0.003, size = 30, normalized size = 0.9 \[ 3\,{\frac{b}{{a}^{2} \left ( b+a\sqrt [3]{x} \right ) }}+3\,{\frac{\ln \left ( b+a\sqrt [3]{x} \right ) }{{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^(1/3))^2/x,x)
[Out]
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Maxima [A] time = 1.43999, size = 46, normalized size = 1.39 \[ -\frac{3}{a^{2} + \frac{a b}{x^{\frac{1}{3}}}} + \frac{3 \, \log \left (a + \frac{b}{x^{\frac{1}{3}}}\right )}{a^{2}} + \frac{\log \left (x\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229404, size = 47, normalized size = 1.42 \[ \frac{3 \,{\left ({\left (a x^{\frac{1}{3}} + b\right )} \log \left (a x^{\frac{1}{3}} + b\right ) + b\right )}}{a^{3} x^{\frac{1}{3}} + a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.9554, size = 99, normalized size = 3. \[ \begin{cases} \frac{3 a x \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} + \frac{3 b x^{\frac{2}{3}} \log{\left (\sqrt [3]{x} + \frac{b}{a} \right )}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} + \frac{3 b x^{\frac{2}{3}}}{a^{3} x + a^{2} b x^{\frac{2}{3}}} & \text{for}\: a \neq 0 \\\frac{3 x^{\frac{2}{3}}}{2 b^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**(1/3))**2/x,x)
[Out]
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GIAC/XCAS [A] time = 0.214898, size = 41, normalized size = 1.24 \[ \frac{3 \,{\rm ln}\left ({\left | a x^{\frac{1}{3}} + b \right |}\right )}{a^{2}} + \frac{3 \, b}{{\left (a x^{\frac{1}{3}} + b\right )} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^(1/3))^2*x),x, algorithm="giac")
[Out]