Optimal. Leaf size=19 \[ 3-e^x+\frac {1}{5 x}-x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 6, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2194} \begin {gather*} -x^2-e^x+\frac {1}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-1-5 e^x x^2-10 x^3}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-5 e^x+\frac {-1-10 x^3}{x^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {-1-10 x^3}{x^2} \, dx-\int e^x \, dx\\ &=-e^x+\frac {1}{5} \int \left (-\frac {1}{x^2}-10 x\right ) \, dx\\ &=-e^x+\frac {1}{5 x}-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.95 \begin {gather*} -e^x+\frac {1}{5 x}-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 17, normalized size = 0.89 \begin {gather*} -\frac {5 \, x^{3} + 5 \, x e^{x} - 1}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 17, normalized size = 0.89 \begin {gather*} -\frac {5 \, x^{3} + 5 \, x e^{x} - 1}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 16, normalized size = 0.84
method | result | size |
default | \(-x^{2}+\frac {1}{5 x}-{\mathrm e}^{x}\) | \(16\) |
risch | \(-x^{2}+\frac {1}{5 x}-{\mathrm e}^{x}\) | \(16\) |
norman | \(\frac {\frac {1}{5}-x^{3}-{\mathrm e}^{x} x}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 0.79 \begin {gather*} -x^{2} + \frac {1}{5 \, x} - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{5\,x}-{\mathrm {e}}^x-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 10, normalized size = 0.53 \begin {gather*} - x^{2} - e^{x} + \frac {1}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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