Optimal. Leaf size=9 \[ \frac {e^{a x}}{a} \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2225}
\begin {gather*} \frac {e^{a x}}{a} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {align*} \int e^{a x} \, dx &=\frac {e^{a x}}{a}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {e^{a x}}{a} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 9, normalized size = 1.00
method | result | size |
gosper | \(\frac {{\mathrm e}^{a x}}{a}\) | \(9\) |
derivativedivides | \(\frac {{\mathrm e}^{a x}}{a}\) | \(9\) |
default | \(\frac {{\mathrm e}^{a x}}{a}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{a x}}{a}\) | \(9\) |
risch | \(\frac {{\mathrm e}^{a x}}{a}\) | \(9\) |
meijerg | \(-\frac {1-{\mathrm e}^{a x}}{a}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.64, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{\left (a x\right )}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.14, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{\left (a x\right )}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} \begin {cases} \frac {e^{a x}}{a} & \text {for}\: a \neq 0 \\x & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.69, size = 8, normalized size = 0.89 \begin {gather*} \frac {e^{\left (a x\right )}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 8, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^{a\,x}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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