Optimal. Leaf size=13 \[ 5 \left (-175+x+\left (e^x+\log (7)\right )^2\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.38, number of steps
used = 3, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2225}
\begin {gather*} 5 x+5 e^{2 x}+10 e^x \log (7) \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 x+10 \int e^{2 x} \, dx+(10 \log (7)) \int e^x \, dx\\ &=5 e^{2 x}+5 x+10 e^x \log (7)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.15 \begin {gather*} 5 \left (e^{2 x}+x+e^x \log (49)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 17, normalized size = 1.31
method | result | size |
default | \(5 x +5 \,{\mathrm e}^{2 x}+10 \ln \left (7\right ) {\mathrm e}^{x}\) | \(17\) |
norman | \(5 x +5 \,{\mathrm e}^{2 x}+10 \ln \left (7\right ) {\mathrm e}^{x}\) | \(17\) |
risch | \(5 x +5 \,{\mathrm e}^{2 x}+10 \ln \left (7\right ) {\mathrm e}^{x}\) | \(17\) |
derivativedivides | \(5 \,{\mathrm e}^{2 x}+10 \ln \left (7\right ) {\mathrm e}^{x}+5 \ln \left ({\mathrm e}^{x}\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 16, normalized size = 1.23 \begin {gather*} 10 \, e^{x} \log \left (7\right ) + 5 \, x + 5 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 16, normalized size = 1.23 \begin {gather*} 10 \, e^{x} \log \left (7\right ) + 5 \, x + 5 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 1.31 \begin {gather*} 5 x + 5 e^{2 x} + 10 e^{x} \log {\left (7 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 16, normalized size = 1.23 \begin {gather*} 10 \, e^{x} \log \left (7\right ) + 5 \, x + 5 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 16, normalized size = 1.23 \begin {gather*} 5\,x+5\,{\mathrm {e}}^{2\,x}+10\,{\mathrm {e}}^x\,\ln \left (7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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