Optimal. Leaf size=20 \[ -x+\frac {20 e^7 x (1+x)}{4+e^5} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.15, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {12} \begin {gather*} \frac {5 e^7 (2 x+1)^2}{4+e^5}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-4-e^5+e^7 (20+40 x)\right ) \, dx}{4+e^5}\\ &=-x+\frac {5 e^7 (1+2 x)^2}{4+e^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.60 \begin {gather*} -\frac {4 x+e^5 x-20 e^7 x-20 e^7 x^2}{4+e^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 25, normalized size = 1.25 \begin {gather*} \frac {20 \, {\left (x^{2} + x\right )} e^{7} - x e^{5} - 4 \, x}{e^{5} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 25, normalized size = 1.25 \begin {gather*} \frac {20 \, {\left (x^{2} + x\right )} e^{7} - x e^{5} - 4 \, x}{e^{5} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.15
method | result | size |
gosper | \(-\frac {x \left (-20 x \,{\mathrm e}^{7}+{\mathrm e}^{5}-20 \,{\mathrm e}^{7}+4\right )}{4+{\mathrm e}^{5}}\) | \(23\) |
default | \(\frac {{\mathrm e}^{7} \left (20 x^{2}+20 x \right )-x \,{\mathrm e}^{5}-4 x}{4+{\mathrm e}^{5}}\) | \(29\) |
norman | \(-\frac {\left ({\mathrm e}^{5}-20 \,{\mathrm e}^{7}+4\right ) x}{4+{\mathrm e}^{5}}+\frac {20 \,{\mathrm e}^{7} x^{2}}{4+{\mathrm e}^{5}}\) | \(32\) |
risch | \(\frac {20 \,{\mathrm e}^{7} x^{2}}{4+{\mathrm e}^{5}}+\frac {20 \,{\mathrm e}^{7} x}{4+{\mathrm e}^{5}}-\frac {{\mathrm e}^{5} x}{4+{\mathrm e}^{5}}-\frac {4 x}{4+{\mathrm e}^{5}}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 25, normalized size = 1.25 \begin {gather*} \frac {20 \, {\left (x^{2} + x\right )} e^{7} - x e^{5} - 4 \, x}{e^{5} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.65, size = 26, normalized size = 1.30 \begin {gather*} \frac {{\mathrm {e}}^{-7}\,{\left ({\mathrm {e}}^5-{\mathrm {e}}^7\,\left (40\,x+20\right )+4\right )}^2}{80\,\left ({\mathrm {e}}^5+4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 29, normalized size = 1.45 \begin {gather*} \frac {20 x^{2} e^{7}}{4 + e^{5}} + \frac {x \left (- e^{5} - 4 + 20 e^{7}\right )}{4 + e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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