Optimal. Leaf size=40 \[ \frac{2}{3} e^{\sqrt{3 x+5}} \sqrt{3 x+5}-\frac{2}{3} e^{\sqrt{3 x+5}} \]
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Rubi [A] time = 0.0123375, antiderivative size = 40, 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 = {2207, 2176, 2194} \[ \frac{2}{3} e^{\sqrt{3 x+5}} \sqrt{3 x+5}-\frac{2}{3} e^{\sqrt{3 x+5}} \]
Antiderivative was successfully verified.
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Rule 2207
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{\sqrt{5+3 x}} \, dx &=\frac{2}{3} \operatorname{Subst}\left (\int e^x x \, dx,x,\sqrt{5+3 x}\right )\\ &=\frac{2}{3} e^{\sqrt{5+3 x}} \sqrt{5+3 x}-\frac{2}{3} \operatorname{Subst}\left (\int e^x \, dx,x,\sqrt{5+3 x}\right )\\ &=-\frac{2}{3} e^{\sqrt{5+3 x}}+\frac{2}{3} e^{\sqrt{5+3 x}} \sqrt{5+3 x}\\ \end{align*}
Mathematica [A] time = 0.0117546, size = 26, normalized size = 0.65 \[ \frac{2}{3} e^{\sqrt{3 x+5}} \left (\sqrt{3 x+5}-1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 29, normalized size = 0.7 \begin{align*} -{\frac{2}{3}{{\rm e}^{\sqrt{5+3\,x}}}}+{\frac{2}{3}{{\rm e}^{\sqrt{5+3\,x}}}\sqrt{5+3\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05085, size = 26, normalized size = 0.65 \begin{align*} \frac{2}{3} \,{\left (\sqrt{3 \, x + 5} - 1\right )} e^{\left (\sqrt{3 \, x + 5}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45192, size = 58, normalized size = 1.45 \begin{align*} \frac{2}{3} \,{\left (\sqrt{3 \, x + 5} - 1\right )} e^{\left (\sqrt{3 \, x + 5}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.181676, size = 34, normalized size = 0.85 \begin{align*} \frac{2 \sqrt{3 x + 5} e^{\sqrt{3 x + 5}}}{3} - \frac{2 e^{\sqrt{3 x + 5}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26458, size = 28, normalized size = 0.7 \begin{align*} \frac{2}{3} \,{\left (\sqrt{3 \, x + 5} - 1\right )} e^{\left (\sqrt{3 \, x + 5}\right )} + \frac{2}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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