Optimal. Leaf size=253 \[ \frac {(x-1)^{4/5} \left (\log \left (\sqrt [5]{x-1}+1\right )+\frac {1}{4} \left (-1-\sqrt {5}\right ) \log \left (2 (x-1)^{2/5}+\left (-1-\sqrt {5}\right ) \sqrt [5]{x-1}+2\right )+\frac {1}{4} \left (\sqrt {5}-1\right ) \log \left (2 (x-1)^{2/5}+\left (\sqrt {5}-1\right ) \sqrt [5]{x-1}+2\right )-\sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} \tan ^{-1}\left (-\frac {4 \sqrt [5]{x-1}}{\sqrt {10-2 \sqrt {5}}}+\frac {1}{\sqrt {10-2 \sqrt {5}}}+\sqrt {\frac {5}{10-2 \sqrt {5}}}\right )+\sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} \tan ^{-1}\left (\frac {4 \sqrt [5]{x-1}}{\sqrt {10+2 \sqrt {5}}}-\frac {1}{\sqrt {10+2 \sqrt {5}}}+\sqrt {\frac {5}{10+2 \sqrt {5}}}\right )\right )}{\sqrt [5]{(x-1)^4}} \]
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Rubi [F] time = 0.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx &=\int \frac {1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx\\ \end {align*}
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Mathematica [C] time = 0.01, size = 27, normalized size = 0.11 \begin {gather*} \frac {5 (x-1) \, _2F_1\left (\frac {1}{5},1;\frac {6}{5};1-x\right )}{\sqrt [5]{(x-1)^4}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 1.19, size = 411, normalized size = 1.62 \begin {gather*} -\sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} \tan ^{-1}\left (\frac {\sqrt {10+2 \sqrt {5}} \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}}{-4+4 x+\left (-1+\sqrt {5}\right ) \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}}\right )+\sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} \tan ^{-1}\left (\frac {\sqrt {10-2 \sqrt {5}} \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}}{4-4 x+\left (1+\sqrt {5}\right ) \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}}\right )-\frac {4}{5} \log (-1+x)+\frac {1}{5} \log \left (1-4 x+6 x^2-4 x^3+x^4\right )+\log \left (-1+x+\sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}\right )+\frac {1}{4} \left (-1-\sqrt {5}\right ) \log \left (2-4 x+2 x^2+\left (1+\sqrt {5} (1-x)-x\right ) \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}+2 \left (1-4 x+6 x^2-4 x^3+x^4\right )^{2/5}\right )+\frac {1}{4} \left (-1+\sqrt {5}\right ) \log \left (2-4 x+2 x^2+\left (1+\sqrt {5} (-1+x)-x\right ) \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}+2 \left (1-4 x+6 x^2-4 x^3+x^4\right )^{2/5}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.27, size = 1084, normalized size = 4.28
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}^{\frac {1}{5}} x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 15.04, size = 10683, normalized size = 42.23
method | result | size |
trager | \(\text {Expression too large to display}\) | \(10683\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}^{\frac {1}{5}} x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {1}{x\,{\left (x^4-4\,x^3+6\,x^2-4\,x+1\right )}^{1/5}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \sqrt [5]{\left (x - 1\right )^{4}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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