Optimal. Leaf size=11 \[ 2 \sqrt {x^2+x} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {629} \begin {gather*} 2 \sqrt {x^2+x} \end {gather*}
Antiderivative was successfully verified.
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Rule 629
Rubi steps
\begin {align*} \int \frac {1+2 x}{\sqrt {x+x^2}} \, dx &=2 \sqrt {x+x^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} 2 \sqrt {x (x+1)} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 11, normalized size = 1.00 \begin {gather*} 2 \sqrt {x^2+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 9, normalized size = 0.82 \begin {gather*} 2 \, \sqrt {x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 9, normalized size = 0.82 \begin {gather*} 2 \, \sqrt {x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.27 \begin {gather*} \frac {2 \left (x +1\right ) x}{\sqrt {x^{2}+x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 9, normalized size = 0.82 \begin {gather*} 2 \, \sqrt {x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.52, size = 9, normalized size = 0.82 \begin {gather*} 2\,\sqrt {x\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 8, normalized size = 0.73 \begin {gather*} 2 \sqrt {x^{2} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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