Optimal. Leaf size=13 \[ \sqrt{2 x^3+x^2} \]
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Rubi [A] time = 0.0097622, antiderivative size = 13, normalized size of antiderivative = 1., 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} \[ \sqrt{2 x^3+x^2} \]
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*}
Mathematica [A] time = 0.0092088, size = 13, normalized size = 1. \[ \sqrt{x^2 (2 x+1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 21, normalized size = 1.6 \begin{align*}{{x}^{2} \left ( 1+2\,x \right ){\frac{1}{\sqrt{2\,{x}^{3}+{x}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.089, size = 15, normalized size = 1.15 \begin{align*} \sqrt{2 \, x^{3} + x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40801, size = 26, normalized size = 2. \begin{align*} \sqrt{2 \, x^{3} + x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.139449, size = 10, normalized size = 0.77 \begin{align*} \sqrt{2 x^{3} + x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14004, size = 15, normalized size = 1.15 \begin{align*} \sqrt{2 \, x^{3} + x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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