Optimal. Leaf size=16 \[ \frac {4 \left (x^6+x\right )^{3/4}}{3 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1590} \begin {gather*} \frac {4 \left (x^6+x\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1590
Rubi steps
\begin {align*} \int \frac {-3+2 x^5}{x^3 \sqrt [4]{x+x^6}} \, dx &=\frac {4 \left (x+x^6\right )^{3/4}}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^6+x\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.22, size = 16, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^6+x\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 12, normalized size = 0.75 \begin {gather*} \frac {4 \, {\left (x^{6} + x\right )}^{\frac {3}{4}}}{3 \, x^{3}} \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 {2 \, x^{5} - 3}{{\left (x^{6} + x\right )}^{\frac {1}{4}} x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 32, normalized size = 2.00 \begin {gather*} \frac {4 \left (1+x \right ) \left (x^{4}-x^{3}+x^{2}-x +1\right )}{3 x^{2} \left (x^{6}+x \right )^{\frac {1}{4}}} \end {gather*}
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 {2 \, x^{5} - 3}{{\left (x^{6} + x\right )}^{\frac {1}{4}} x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 12, normalized size = 0.75 \begin {gather*} \frac {4\,{\left (x^6+x\right )}^{3/4}}{3\,x^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 {2 x^{5} - 3}{x^{3} \sqrt [4]{x \left (x + 1\right ) \left (x^{4} - x^{3} + x^{2} - x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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