Optimal. Leaf size=26 \[ 8+e^{4+e^4+(16-x)^2}-5 e^{3 x}+2 x \]
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Rubi [A]
time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.92, number of steps
used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2225, 2268}
\begin {gather*} e^{x^2-32 x+e^4+260}+2 x-5 e^{3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2268
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x-15 \int e^{3 x} \, dx+\int e^{260+e^4-32 x+x^2} (-32+2 x) \, dx\\ &=-5 e^{3 x}+e^{260+e^4-32 x+x^2}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 24, normalized size = 0.92 \begin {gather*} -5 e^{3 x}+e^{260+e^4-32 x+x^2}+2 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 22, normalized size = 0.85
method | result | size |
default | \(2 x +{\mathrm e}^{{\mathrm e}^{4}+x^{2}-32 x +260}-5 \,{\mathrm e}^{3 x}\) | \(22\) |
norman | \(2 x +{\mathrm e}^{{\mathrm e}^{4}+x^{2}-32 x +260}-5 \,{\mathrm e}^{3 x}\) | \(22\) |
risch | \(2 x +{\mathrm e}^{{\mathrm e}^{4}+x^{2}-32 x +260}-5 \,{\mathrm e}^{3 x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + e^{\left (x^{2} - 32 \, x + e^{4} + 260\right )} - 5 \, e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + e^{\left (x^{2} - 32 \, x + e^{4} + 260\right )} - 5 \, e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 0.85 \begin {gather*} 2 x - 5 e^{3 x} + e^{x^{2} - 32 x + e^{4} + 260} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + e^{\left (x^{2} - 32 \, x + e^{4} + 260\right )} - 5 \, e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.19, size = 24, normalized size = 0.92 \begin {gather*} 2\,x-5\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{-32\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{260}\,{\mathrm {e}}^{{\mathrm {e}}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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