Optimal. Leaf size=19 \[ \frac {5 (x-1) (x+5)}{6 \sqrt [5]{(x-1)^4}} \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.74, number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {1680, 15, 43} \begin {gather*} \frac {5 (x-1)^2}{6 \sqrt [5]{(x-1)^4}}+\frac {5 (x-1)}{\sqrt [5]{(x-1)^4}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 43
Rule 1680
Rubi steps
\begin {align*} \int \frac {x}{\sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx &=\operatorname {Subst}\left (\int \frac {1+x}{\sqrt [5]{x^4}} \, dx,x,-1+x\right )\\ &=\frac {(-1+x)^{4/5} \operatorname {Subst}\left (\int \frac {1+x}{x^{4/5}} \, dx,x,-1+x\right )}{\sqrt [5]{(-1+x)^4}}\\ &=\frac {(-1+x)^{4/5} \operatorname {Subst}\left (\int \left (\frac {1}{x^{4/5}}+\sqrt [5]{x}\right ) \, dx,x,-1+x\right )}{\sqrt [5]{(-1+x)^4}}\\ &=-\frac {5 (1-x)}{\sqrt [5]{(-1+x)^4}}+\frac {5 (1-x)^2}{6 \sqrt [5]{(-1+x)^4}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {5 (x-1) (x+5)}{6 \sqrt [5]{(x-1)^4}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 5.79, size = 19, normalized size = 1.00 \begin {gather*} \frac {5 (x-1) (x+5)}{6 \sqrt [5]{(x-1)^4}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.39, size = 40, normalized size = 2.11 \begin {gather*} \frac {5 \, {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}^{\frac {4}{5}} {\left (x + 5\right )}}{6 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \end {gather*}
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 {x}{{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}^{\frac {1}{5}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 1.53 \begin {gather*} \frac {5 \left (-1+x \right ) \left (5+x \right )}{6 \left (x^{4}-4 x^{3}+6 x^{2}-4 x +1\right )^{\frac {1}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 15, normalized size = 0.79 \begin {gather*} \frac {5 \, {\left (x^{2} + 4 \, x - 5\right )}}{6 \, {\left (x - 1\right )}^{\frac {4}{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 30, normalized size = 1.58 \begin {gather*} \frac {5\,\left (x+5\right )\,{\left (x^4-4\,x^3+6\,x^2-4\,x+1\right )}^{4/5}}{6\,{\left (x-1\right )}^3} \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 {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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