Optimal. Leaf size=176 \[ \frac{\log (1-(2-k) x)}{2^{2/3} \sqrt [3]{1-k}}+\frac{\log (1-k x)}{2\ 2^{2/3} \sqrt [3]{1-k}}-\frac{3 \log \left (k x+2^{2/3} \sqrt [3]{1-k} \sqrt [3]{(1-x) x (1-k x)}-1\right )}{2\ 2^{2/3} \sqrt [3]{1-k}}-\frac{\sqrt{3} \tan ^{-1}\left (\frac{\frac{\sqrt [3]{2} (1-k x)}{\sqrt [3]{1-k} \sqrt [3]{(1-x) x (1-k x)}}+1}{\sqrt{3}}\right )}{2^{2/3} \sqrt [3]{1-k}} \]
[Out]
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Rubi [F] time = 0.819896, 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. \[ \text{Int}\left (\frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)),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((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))**(2/3),x)
[Out]
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Mathematica [A] time = 0.41476, size = 0, normalized size = 0. \[ \int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(1 - k*x)/((1 + (-2 + k)*x)*((1 - x)*x*(1 - k*x))^(2/3)),x]
[Out]
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Maple [F] time = 0.073, size = 0, normalized size = 0. \[ \int{\frac{-kx+1}{1+ \left ( -2+k \right ) x} \left ( \left ( 1-x \right ) x \left ( -kx+1 \right ) \right ) ^{-{\frac{2}{3}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(2/3),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ -\int \frac{k x - 1}{\left ({\left (k x - 1\right )}{\left (x - 1\right )} x\right )^{\frac{2}{3}}{\left ({\left (k - 2\right )} x + 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(k*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((k - 2)*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*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((k - 2)*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((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int -\frac{k x - 1}{\left ({\left (k x - 1\right )}{\left (x - 1\right )} x\right )^{\frac{2}{3}}{\left ({\left (k - 2\right )} x + 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(k*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((k - 2)*x + 1)),x, algorithm="giac")
[Out]