Optimal. Leaf size=27 \[ \frac {-4+e^3+\frac {1}{4} \left (-2+e^{x+x^2}\right )-\frac {7 x}{3}}{x} \]
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Rubi [A]
time = 0.06, antiderivative size = 29, normalized size of antiderivative = 1.07, number of steps
used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14, 2327}
\begin {gather*} \frac {e^{x^2+x}}{4 x}-\frac {9-2 e^3}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2327
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {18-4 e^3+e^{x+x^2} \left (-1+x+2 x^2\right )}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-\frac {2 \left (-9+2 e^3\right )}{x^2}+\frac {e^{x+x^2} (1+x) (-1+2 x)}{x^2}\right ) \, dx\\ &=-\frac {9-2 e^3}{2 x}+\frac {1}{4} \int \frac {e^{x+x^2} (1+x) (-1+2 x)}{x^2} \, dx\\ &=\frac {e^{x+x^2}}{4 x}-\frac {9-2 e^3}{2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.59, size = 21, normalized size = 0.78 \begin {gather*} \frac {-18+4 e^3+e^{x+x^2}}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 17, normalized size = 0.63
method | result | size |
norman | \(\frac {\frac {{\mathrm e}^{x^{2}+x}}{4}+{\mathrm e}^{3}-\frac {9}{2}}{x}\) | \(17\) |
risch | \(\frac {{\mathrm e}^{3}}{x}-\frac {9}{2 x}+\frac {{\mathrm e}^{\left (x +1\right ) x}}{4 x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.63 \begin {gather*} \frac {4 \, e^{3} + e^{\left (x^{2} + x\right )} - 18}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.63 \begin {gather*} \frac {e^{x^{2} + x}}{4 x} - \frac {\frac {9}{2} - e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 17, normalized size = 0.63 \begin {gather*} \frac {4 \, e^{3} + e^{\left (x^{2} + x\right )} - 18}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 17, normalized size = 0.63 \begin {gather*} \frac {{\mathrm {e}}^{x^2+x}+4\,{\mathrm {e}}^3-18}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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