Optimal. Leaf size=14 \[ -e^3+e^5+e^{4 x} \]
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Rubi [A]
time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.36, number of steps
used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225}
\begin {gather*} e^{4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int e^{4 x} \, dx\\ &=e^{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 5, normalized size = 0.36 \begin {gather*} e^{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 5, normalized size = 0.36
method | result | size |
gosper | \({\mathrm e}^{4 x}\) | \(5\) |
derivativedivides | \({\mathrm e}^{4 x}\) | \(5\) |
default | \({\mathrm e}^{4 x}\) | \(5\) |
norman | \({\mathrm e}^{4 x}\) | \(5\) |
risch | \({\mathrm e}^{4 x}\) | \(5\) |
meijerg | \({\mathrm e}^{4 x}-1\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 4, normalized size = 0.29 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 4, normalized size = 0.29 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 3, normalized size = 0.21 \begin {gather*} e^{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 4, normalized size = 0.29 \begin {gather*} e^{\left (4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 4, normalized size = 0.29 \begin {gather*} {\mathrm {e}}^{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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