Optimal. Leaf size=253 \[ \frac {(x-1)^{4/5} \left (\log \left (\sqrt [5]{x-1}+1\right )+\frac {1}{4} \left (-1-\sqrt {5}\right ) \log \left (2 (x-1)^{2/5}+\left (-1-\sqrt {5}\right ) \sqrt [5]{x-1}+2\right )+\frac {1}{4} \left (\sqrt {5}-1\right ) \log \left (2 (x-1)^{2/5}+\left (\sqrt {5}-1\right ) \sqrt [5]{x-1}+2\right )-\sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} \tan ^{-1}\left (-\frac {4 \sqrt [5]{x-1}}{\sqrt {10-2 \sqrt {5}}}+\frac {1}{\sqrt {10-2 \sqrt {5}}}+\sqrt {\frac {5}{10-2 \sqrt {5}}}\right )+\sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} \tan ^{-1}\left (\frac {4 \sqrt [5]{x-1}}{\sqrt {10+2 \sqrt {5}}}-\frac {1}{\sqrt {10+2 \sqrt {5}}}+\sqrt {\frac {5}{10+2 \sqrt {5}}}\right )\right )}{\sqrt [5]{(x-1)^4}} \]
________________________________________________________________________________________
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.
[In]
[Out]
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*}
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 1.21, size = 411, normalized size = 1.62 \begin {gather*} \frac {1}{5} \log \left (x^4-4 x^3+6 x^2-4 x+1\right )+\log \left (\sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}+x-1\right )+\frac {1}{4} \left (-1-\sqrt {5}\right ) \log \left (2 x^2+2 \left (x^4-4 x^3+6 x^2-4 x+1\right )^{2/5}+\left (\sqrt {5} (1-x)-x+1\right ) \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}-4 x+2\right )+\frac {1}{4} \left (\sqrt {5}-1\right ) \log \left (2 x^2+2 \left (x^4-4 x^3+6 x^2-4 x+1\right )^{2/5}+\left (\sqrt {5} (x-1)-x+1\right ) \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}-4 x+2\right )-\sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} \tan ^{-1}\left (\frac {\sqrt {10+2 \sqrt {5}} \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}}{\left (\sqrt {5}-1\right ) \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}+4 x-4}\right )+\sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} \tan ^{-1}\left (\frac {\sqrt {10-2 \sqrt {5}} \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}}{\left (1+\sqrt {5}\right ) \sqrt [5]{x^4-4 x^3+6 x^2-4 x+1}-4 x+4}\right )-\frac {4}{5} \log (x-1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.81, size = 1084, normalized size = 4.28
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 11.89, size = 11302, normalized size = 44.67 \begin {gather*} \text {output too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________