Optimal. Leaf size=16 \[ 2+5 e^{-x+81 (2+x)}+x \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2280, 45}
\begin {gather*} x+5 e^{80 x+162} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2280
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{80} \text {Subst}\left (\int \frac {400+x}{x^2} \, dx,x,e^{-162-80 x}\right )\right )\\ &=-\left (\frac {1}{80} \text {Subst}\left (\int \left (\frac {400}{x^2}+\frac {1}{x}\right ) \, dx,x,e^{-162-80 x}\right )\right )\\ &=5 e^{162+80 x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 0.69 \begin {gather*} 5 e^{162+80 x}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 21, normalized size = 1.31
method | result | size |
risch | \(x +5 \,{\mathrm e}^{80 x +162}\) | \(11\) |
norman | \(\left (5+x \,{\mathrm e}^{-80 x -162}\right ) {\mathrm e}^{80 x +162}\) | \(20\) |
derivativedivides | \(5 \,{\mathrm e}^{80 x +162}-\frac {\ln \left ({\mathrm e}^{-80 x -162}\right )}{80}\) | \(21\) |
default | \(5 \,{\mathrm e}^{80 x +162}-\frac {\ln \left ({\mathrm e}^{-80 x -162}\right )}{80}\) | \(21\) |
meijerg | \(-\frac {{\mathrm e}^{80 x -80 x \,{\mathrm e}^{162}-162} \left (1-{\mathrm e}^{80 x \,{\mathrm e}^{162} \left (1-{\mathrm e}^{-162}\right )}\right )}{80 \left (1-{\mathrm e}^{-162}\right )}-5 \,{\mathrm e}^{80 x -80 x \,{\mathrm e}^{162}} \left (1-{\mathrm e}^{80 x \,{\mathrm e}^{162}}\right )\) | \(61\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 11, normalized size = 0.69 \begin {gather*} x + 5 \, e^{\left (80 \, x + 162\right )} + \frac {81}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 10, normalized size = 0.62 \begin {gather*} x + 5 \, e^{\left (80 \, x + 162\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.50 \begin {gather*} x + 5 e^{80 x + 162} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 10, normalized size = 0.62 \begin {gather*} x + 5 \, e^{\left (80 \, x + 162\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 10, normalized size = 0.62 \begin {gather*} x+5\,{\mathrm {e}}^{80\,x}\,{\mathrm {e}}^{162} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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