Optimal. Leaf size=13 \[ \frac {e^{(2+a) x}}{2+a} \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2259, 2225}
\begin {gather*} \frac {e^{(a+2) x}}{a+2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2259
Rubi steps
\begin {align*} \int e^{2 x+a x} \, dx &=\int e^{(2+a) x} \, dx\\ &=\frac {e^{(2+a) x}}{2+a}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {e^{(2+a) x}}{2+a} \end {gather*}
Antiderivative was successfully verified.
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Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 1.80, size = 20, normalized size = 1.54 \begin {gather*} \text {Piecewise}\left [\left \{\left \{\frac {E^{x \left (2+a\right )}}{2+a},a\text {!=}-2\right \}\right \},x\right ] \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.01, size = 15, normalized size = 1.15
method | result | size |
risch | \(\frac {{\mathrm e}^{\left (2+a \right ) x}}{2+a}\) | \(13\) |
gosper | \(\frac {{\mathrm e}^{a x +2 x}}{2+a}\) | \(15\) |
derivativedivides | \(\frac {{\mathrm e}^{a x +2 x}}{2+a}\) | \(15\) |
default | \(\frac {{\mathrm e}^{a x +2 x}}{2+a}\) | \(15\) |
norman | \(\frac {{\mathrm e}^{a x +2 x}}{2+a}\) | \(15\) |
meijerg | \(\frac {1-{\mathrm e}^{-x \left (-a -2\right )}}{-a -2}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 1.08 \begin {gather*} \frac {e^{\left (a x + 2 \, x\right )}}{a + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 12, normalized size = 0.92 \begin {gather*} \frac {e^{\left ({\left (a + 2\right )} x\right )}}{a + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 1.08 \begin {gather*} \begin {cases} \frac {e^{a x + 2 x}}{a + 2} & \text {for}\: a \neq -2 \\x & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {\mathrm {e}^{a x+2 x}}{a+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 14, normalized size = 1.08 \begin {gather*} \frac {{\mathrm {e}}^{2\,x+a\,x}}{a+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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