Optimal. Leaf size=12 \[ x-\frac {15 x^{7/3}}{e^{11}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \begin {gather*} x-\frac {15 x^{7/3}}{e^{11}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e^6-\frac {35 x^{4/3}}{e^5}\right ) \, dx}{e^6}\\ &=x-\frac {15 x^{7/3}}{e^{11}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} x-\frac {15 x^{7/3}}{e^{11}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 15, normalized size = 1.25 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} - x e^{11}\right )} e^{\left (-11\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 17, normalized size = 1.42 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} e^{\left (-5\right )} - x e^{6}\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 24, normalized size = 2.00
method | result | size |
default | \({\mathrm e}^{-2} {\mathrm e}^{-4} \left ({\mathrm e}^{2} {\mathrm e}^{4} x -15 x^{\frac {7}{3}} {\mathrm e}^{-5}\right )\) | \(24\) |
derivativedivides | \(3 \,{\mathrm e}^{-2} {\mathrm e}^{-4} \left (\frac {{\mathrm e}^{2} {\mathrm e}^{4} x}{3}-5 x^{\frac {7}{3}} {\mathrm e}^{-5}\right )\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 17, normalized size = 1.42 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} e^{\left (-5\right )} - x e^{6}\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.23, size = 9, normalized size = 0.75 \begin {gather*} x-15\,x^{7/3}\,{\mathrm {e}}^{-11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.59, size = 17, normalized size = 1.42 \begin {gather*} \frac {- \frac {15 x^{\frac {7}{3}}}{e^{5}} + x e^{6}}{e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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