Optimal. Leaf size=22 \[ \frac {3 x \left (4-x-401 x^2\right )}{e^5+x^2} \]
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Rubi [A] time = 0.03, antiderivative size = 28, normalized size of antiderivative = 1.27, number of steps used = 4, number of rules used = 4, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.093, Rules used = {28, 1814, 21, 8} \begin {gather*} \frac {3 \left (\left (4+401 e^5\right ) x+e^5\right )}{x^2+e^5}-1203 x \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 21
Rule 28
Rule 1814
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-12 x^2-1203 x^4+e^5 \left (12-6 x-3609 x^2\right )}{\left (e^5+x^2\right )^2} \, dx\\ &=\frac {3 \left (e^5+\left (4+401 e^5\right ) x\right )}{e^5+x^2}-\frac {\int \frac {2406 e^{10}+2406 e^5 x^2}{e^5+x^2} \, dx}{2 e^5}\\ &=\frac {3 \left (e^5+\left (4+401 e^5\right ) x\right )}{e^5+x^2}-1203 \int 1 \, dx\\ &=-1203 x+\frac {3 \left (e^5+\left (4+401 e^5\right ) x\right )}{e^5+x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.05 \begin {gather*} \frac {3 \left (e^5+4 x-401 x^3\right )}{e^5+x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 23, normalized size = 1.05 \begin {gather*} -\frac {3 \, {\left (401 \, x^{3} - 4 \, x - e^{5}\right )}}{x^{2} + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 1.00
method | result | size |
gosper | \(\frac {12 x -1203 x^{3}+3 \,{\mathrm e}^{5}}{x^{2}+{\mathrm e}^{5}}\) | \(22\) |
norman | \(\frac {12 x -1203 x^{3}+3 \,{\mathrm e}^{5}}{x^{2}+{\mathrm e}^{5}}\) | \(23\) |
risch | \(-1203 x +\frac {\left (1203 \,{\mathrm e}^{5}+12\right ) x +3 \,{\mathrm e}^{5}}{x^{2}+{\mathrm e}^{5}}\) | \(27\) |
default | \(-1203 x -\frac {3 \left (-\frac {{\mathrm e}^{-5} \left (802 \,{\mathrm e}^{10}+8 \,{\mathrm e}^{5}\right ) x}{2}-{\mathrm e}^{5}\right )}{x^{2}+{\mathrm e}^{5}}\) | \(68\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 25, normalized size = 1.14 \begin {gather*} -1203 \, x + \frac {3 \, {\left (x {\left (401 \, e^{5} + 4\right )} + e^{5}\right )}}{x^{2} + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 21, normalized size = 0.95 \begin {gather*} \frac {3\,\left (-401\,x^3+4\,x+{\mathrm {e}}^5\right )}{x^2+{\mathrm {e}}^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 26, normalized size = 1.18 \begin {gather*} - 1203 x - \frac {x \left (- 1203 e^{5} - 12\right ) - 3 e^{5}}{x^{2} + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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