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 = 0.01, 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 = {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 2176
Rule 2194
Rule 2207
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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.41, size = 19, normalized size = 0.48 \[ \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 19, normalized size = 0.48 \[ \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 29, normalized size = 0.72 \[ -\frac {2 \,{\mathrm e}^{\sqrt {3 x +5}}}{3}+\frac {2 \sqrt {3 x +5}\, {\mathrm e}^{\sqrt {3 x +5}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 19, normalized size = 0.48 \[ \frac {2}{3} \, {\left (\sqrt {3 \, x + 5} - 1\right )} e^{\left (\sqrt {3 \, x + 5}\right )} \]
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 \[ \frac {2\,{\mathrm {e}}^{\sqrt {3\,x+5}}\,\left (\sqrt {3\,x+5}-1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 34, normalized size = 0.85 \[ \frac {2 \sqrt {3 x + 5} e^{\sqrt {3 x + 5}}}{3} - \frac {2 e^{\sqrt {3 x + 5}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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