Optimal. Leaf size=111 \[ \frac{\log (x)}{2 \sqrt [3]{k}}+\frac{\log (1-(k+1) x)}{2 \sqrt [3]{k}}-\frac{3 \log \left (\sqrt [3]{(1-x) x (1-k x)}-\sqrt [3]{k} x\right )}{2 \sqrt [3]{k}}+\frac{\sqrt{3} \tan ^{-1}\left (\frac{\frac{2 \sqrt [3]{k} x}{\sqrt [3]{(1-x) x (1-k x)}}+1}{\sqrt{3}}\right )}{\sqrt [3]{k}} \]
[Out]
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Rubi [F] time = 1.33793, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2-(1+k)*x)/((1-x)*x*(-k*x+1))**(1/3)/(1-(1+k)*x),x)
[Out]
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Mathematica [A] time = 1.23486, size = 0, normalized size = 0. \[ \int \frac{2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(2 - (1 + k)*x)/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - (1 + k)*x)),x]
[Out]
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Maple [F] time = 0.062, size = 0, normalized size = 0. \[ \int{\frac{2- \left ( 1+k \right ) x}{1- \left ( 1+k \right ) x}{\frac{1}{\sqrt [3]{ \left ( 1-x \right ) x \left ( -kx+1 \right ) }}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2-(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (k + 1\right )} x - 2}{\left ({\left (k x - 1\right )}{\left (x - 1\right )} x\right )^{\frac{1}{3}}{\left ({\left (k + 1\right )} x - 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((k + 1)*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((k + 1)*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2-(1+k)*x)/((1-x)*x*(-k*x+1))**(1/3)/(1-(1+k)*x),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (k + 1\right )} x - 2}{\left ({\left (k x - 1\right )}{\left (x - 1\right )} x\right )^{\frac{1}{3}}{\left ({\left (k + 1\right )} x - 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((k + 1)*x - 1)),x, algorithm="giac")
[Out]