Optimal. Leaf size=20 \[ 1+\left (4+2^{e^x x}\right )^2+2 x-4 \log (5) \]
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Rubi [A]
time = 0.12, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps
used = 3, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6838}
\begin {gather*} 2 x+2^{2 e^x x}+2^{e^x x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+\log (2) \int 2^{2 e^x x} e^x (2+2 x) \, dx+\log (2) \int 2^{e^x x} e^x (8+8 x) \, dx\\ &=2^{2 e^x x}+2^{3+e^x x}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 15, normalized size = 0.75 \begin {gather*} \left (4+2^{e^x x}\right )^2+2 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 23, normalized size = 1.15
method | result | size |
risch | \(2 x +2^{2 \,{\mathrm e}^{x} x}+8 \,2^{{\mathrm e}^{x} x}\) | \(21\) |
default | \(2 x +{\mathrm e}^{2 x \ln \left (2\right ) {\mathrm e}^{x}}+8 \,{\mathrm e}^{x \ln \left (2\right ) {\mathrm e}^{x}}\) | \(23\) |
norman | \(2 x +{\mathrm e}^{2 x \ln \left (2\right ) {\mathrm e}^{x}}+8 \,{\mathrm e}^{x \ln \left (2\right ) {\mathrm e}^{x}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 19, normalized size = 0.95 \begin {gather*} 2^{2 \, x e^{x}} + 8 \cdot 2^{x e^{x}} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 19, normalized size = 0.95 \begin {gather*} 2^{2 \, x e^{x}} + 8 \cdot 2^{x e^{x}} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 26, normalized size = 1.30 \begin {gather*} 2 x + e^{2 x e^{x} \log {\left (2 \right )}} + 8 e^{x e^{x} \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 19, normalized size = 0.95 \begin {gather*} 2^{2 \, x e^{x}} + 8 \cdot 2^{x e^{x}} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 19, normalized size = 0.95 \begin {gather*} 2\,x+8\,2^{x\,{\mathrm {e}}^x}+2^{2\,x\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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