Optimal. Leaf size=18 \[ \frac {16 x^2}{\frac {1}{4} \left (3+e^{32}\right )+x} \]
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Rubi [A] time = 0.06, antiderivative size = 22, normalized size of antiderivative = 1.22, number of steps used = 5, number of rules used = 5, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6, 1593, 1983, 27, 74} \begin {gather*} \frac {16 \left (2 x+e^{32}+3\right )^2}{4 x+e^{32}+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 27
Rule 74
Rule 1593
Rule 1983
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (384+128 e^{32}\right ) x+256 x^2}{9+e^{64}+24 x+16 x^2+e^{32} (6+8 x)} \, dx\\ &=\int \frac {x \left (384+128 e^{32}+256 x\right )}{9+e^{64}+24 x+16 x^2+e^{32} (6+8 x)} \, dx\\ &=\int \frac {x \left (128 \left (3+e^{32}\right )+256 x\right )}{\left (3+e^{32}\right )^2+8 \left (3+e^{32}\right ) x+16 x^2} \, dx\\ &=\int \frac {x \left (128 \left (3+e^{32}\right )+256 x\right )}{\left (3+e^{32}+4 x\right )^2} \, dx\\ &=\frac {16 \left (3+e^{32}+2 x\right )^2}{3+e^{32}+4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 36, normalized size = 2.00 \begin {gather*} 128 \left (\frac {\left (3+e^{32}\right )^2}{32 \left (3+e^{32}+4 x\right )}+\frac {1}{32} \left (3+e^{32}+4 x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 32, normalized size = 1.78 \begin {gather*} \frac {4 \, {\left (16 \, x^{2} + 2 \, {\left (2 \, x + 3\right )} e^{32} + 12 \, x + e^{64} + 9\right )}}{4 \, x + e^{32} + 3} \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 = 0.12, size = 17, normalized size = 0.94
method | result | size |
gosper | \(\frac {64 x^{2}}{{\mathrm e}^{32}+4 x +3}\) | \(17\) |
norman | \(\frac {64 x^{2}}{{\mathrm e}^{32}+4 x +3}\) | \(17\) |
risch | \(16 x +\frac {4 \,{\mathrm e}^{64}}{{\mathrm e}^{32}+4 x +3}+\frac {24 \,{\mathrm e}^{32}}{{\mathrm e}^{32}+4 x +3}+\frac {36}{{\mathrm e}^{32}+4 x +3}\) | \(42\) |
meijerg | \(\frac {\left (128 \,{\mathrm e}^{32}+384\right ) \left (-\frac {4 x}{\left ({\mathrm e}^{32}+3\right ) \left (1+\frac {4 x}{{\mathrm e}^{32}+3}\right )}+\ln \left (1+\frac {4 x}{{\mathrm e}^{32}+3}\right )\right )}{16}+\frac {\left ({\mathrm e}^{32}+3\right )^{2} \left (\frac {4 x \left (\frac {12 x}{{\mathrm e}^{32}+3}+6\right )}{3 \left ({\mathrm e}^{32}+3\right ) \left (1+\frac {4 x}{{\mathrm e}^{32}+3}\right )}-2 \ln \left (1+\frac {4 x}{{\mathrm e}^{32}+3}\right )\right )}{\frac {{\mathrm e}^{32}}{4}+\frac {3}{4}}\) | \(108\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 23, normalized size = 1.28 \begin {gather*} 16 \, x + \frac {4 \, {\left (e^{64} + 6 \, e^{32} + 9\right )}}{4 \, x + e^{32} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.18, size = 24, normalized size = 1.33 \begin {gather*} 16\,x+\frac {24\,{\mathrm {e}}^{32}+4\,{\mathrm {e}}^{64}+36}{4\,x+{\mathrm {e}}^{32}+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 22, normalized size = 1.22 \begin {gather*} 16 x + \frac {36 + 24 e^{32} + 4 e^{64}}{4 x + 3 + e^{32}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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