Optimal. Leaf size=24 \[ 4-x-\frac {15 x^2}{4}+\frac {1}{5} \left (-3+4 e^x+x\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2194} \begin {gather*} -\frac {15 x^2}{4}-\frac {4 x}{5}+\frac {4 e^x}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \left (-8+8 e^x-75 x\right ) \, dx\\ &=-\frac {4 x}{5}-\frac {15 x^2}{4}+\frac {4 \int e^x \, dx}{5}\\ &=\frac {4 e^x}{5}-\frac {4 x}{5}-\frac {15 x^2}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.83 \begin {gather*} \frac {1}{10} \left (8 e^x-8 x-\frac {75 x^2}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 13, normalized size = 0.54 \begin {gather*} -\frac {15}{4} \, x^{2} - \frac {4}{5} \, x + \frac {4}{5} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 13, normalized size = 0.54 \begin {gather*} -\frac {15}{4} \, x^{2} - \frac {4}{5} \, x + \frac {4}{5} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.58
method | result | size |
default | \(-\frac {4 x}{5}-\frac {15 x^{2}}{4}+\frac {4 \,{\mathrm e}^{x}}{5}\) | \(14\) |
norman | \(-\frac {4 x}{5}-\frac {15 x^{2}}{4}+\frac {4 \,{\mathrm e}^{x}}{5}\) | \(14\) |
risch | \(-\frac {4 x}{5}-\frac {15 x^{2}}{4}+\frac {4 \,{\mathrm e}^{x}}{5}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 13, normalized size = 0.54 \begin {gather*} -\frac {15}{4} \, x^{2} - \frac {4}{5} \, x + \frac {4}{5} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 0.54 \begin {gather*} \frac {4\,{\mathrm {e}}^x}{5}-\frac {4\,x}{5}-\frac {15\,x^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 17, normalized size = 0.71 \begin {gather*} - \frac {15 x^{2}}{4} - \frac {4 x}{5} + \frac {4 e^{x}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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