Optimal. Leaf size=12 \[ -\frac {9}{4}+e^x+\frac {7 x}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {7 x}{2}+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (7+2 e^x\right ) \, dx\\ &=\frac {7 x}{2}+\int e^x \, dx\\ &=e^x+\frac {7 x}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} e^x+\frac {7 x}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.58
method | result | size |
default | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
norman | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
risch | \(\frac {7 x}{2}+{\mathrm e}^{x}\) | \(7\) |
derivativedivides | \({\mathrm e}^{x}+\frac {7 \ln \left ({\mathrm e}^{x}\right )}{2}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 6, normalized size = 0.50 \begin {gather*} \frac {7\,x}{2}+{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 7, normalized size = 0.58 \begin {gather*} \frac {7 x}{2} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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