Optimal. Leaf size=40 \[ -\frac {2}{3} e^{\sqrt {5+3 x}}+\frac {2}{3} e^{\sqrt {5+3 x}} \sqrt {5+3 x} \]
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Rubi [A]
time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, 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 = {2238, 2207,
2225} \begin {gather*} \frac {2}{3} e^{\sqrt {3 x+5}} \sqrt {3 x+5}-\frac {2}{3} e^{\sqrt {3 x+5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 2238
Rubi steps
\begin {align*} \int e^{\sqrt {5+3 x}} \, dx &=\frac {2}{3} \text {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} \text {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*}
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Mathematica [A]
time = 0.02, size = 26, normalized size = 0.65 \begin {gather*} \frac {2}{3} e^{\sqrt {5+3 x}} \left (-1+\sqrt {5+3 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 29, normalized size = 0.72
method | result | size |
derivativedivides | \(-\frac {2 \,{\mathrm e}^{\sqrt {5+3 x}}}{3}+\frac {2 \,{\mathrm e}^{\sqrt {5+3 x}} \sqrt {5+3 x}}{3}\) | \(29\) |
default | \(-\frac {2 \,{\mathrm e}^{\sqrt {5+3 x}}}{3}+\frac {2 \,{\mathrm e}^{\sqrt {5+3 x}} \sqrt {5+3 x}}{3}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 0.48 \begin {gather*} \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 19, normalized size = 0.48 \begin {gather*} \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 34, normalized size = 0.85 \begin {gather*} \frac {2 \sqrt {3 x + 5} e^{\sqrt {3 x + 5}}}{3} - \frac {2 e^{\sqrt {3 x + 5}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.37, size = 19, normalized size = 0.48 \begin {gather*} \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 19, normalized size = 0.48 \begin {gather*} \frac {2\,{\mathrm {e}}^{\sqrt {3\,x+5}}\,\left (\sqrt {3\,x+5}-1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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