Optimal. Leaf size=20 \[ \frac{1}{5} (5 x+3) \sqrt{(5 x+3)^2} \]
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Rubi [A] time = 0.0045488, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273, Rules used = {247, 15, 30} \[ \frac{1}{5} (5 x+3) \sqrt{(5 x+3)^2} \]
Antiderivative was successfully verified.
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Rule 247
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt{(6+10 x)^2} \, dx &=\frac{1}{10} \operatorname{Subst}\left (\int \sqrt{x^2} \, dx,x,6+10 x\right )\\ &=\frac{\sqrt{(6+10 x)^2} \operatorname{Subst}(\int x \, dx,x,6+10 x)}{10 (6+10 x)}\\ &=\frac{1}{5} (3+5 x) \sqrt{(3+5 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0054408, size = 25, normalized size = 1.25 \[ \frac{x \sqrt{(5 x+3)^2} (5 x+6)}{5 x+3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 24, normalized size = 1.2 \begin{align*}{\frac{x \left ( 5\,x+6 \right ) }{3+5\,x}\sqrt{ \left ( 3+5\,x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.45662, size = 39, normalized size = 1.95 \begin{align*} \sqrt{25 \, x^{2} + 30 \, x + 9} x + \frac{3}{5} \, \sqrt{25 \, x^{2} + 30 \, x + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2315, size = 18, normalized size = 0.9 \begin{align*} 5 \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067217, size = 7, normalized size = 0.35 \begin{align*} 5 x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10032, size = 34, normalized size = 1.7 \begin{align*}{\left (5 \, x^{2} + 6 \, x\right )} \mathrm{sgn}\left (5 \, x + 3\right ) + \frac{9}{5} \, \mathrm{sgn}\left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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