Optimal. Leaf size=13 \[ \sqrt {2 x^3+x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1588} \begin {gather*} \sqrt {2 x^3+x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \frac {x+3 x^2}{\sqrt {x^2+2 x^3}} \, dx &=\sqrt {x^2+2 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \sqrt {x^2 (2 x+1)} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} \sqrt {2 x^3+x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 11, normalized size = 0.85 \begin {gather*} \sqrt {2 \, x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 11, normalized size = 0.85 \begin {gather*} \sqrt {2 \, x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 1.62 \begin {gather*} \frac {\left (2 x +1\right ) x^{2}}{\sqrt {2 x^{3}+x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 11, normalized size = 0.85 \begin {gather*} \sqrt {2 \, x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.23, size = 10, normalized size = 0.77 \begin {gather*} \relax |x|\,\sqrt {2\,x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 10, normalized size = 0.77 \begin {gather*} \sqrt {2 x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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