Optimal. Leaf size=16 \[ \frac {15 \left (e^4+x^2\right )}{-\frac {3}{4}+x} \]
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Rubi [A] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 1.38, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {27, 683} \begin {gather*} 15 x-\frac {15 \left (9+16 e^4\right )}{4 (3-4 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 683
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-240 e^4-360 x+240 x^2}{(-3+4 x)^2} \, dx\\ &=\int \left (15-\frac {15 \left (9+16 e^4\right )}{(-3+4 x)^2}\right ) \, dx\\ &=-\frac {15 \left (9+16 e^4\right )}{4 (3-4 x)}+15 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.50 \begin {gather*} -\frac {120 \left (9+8 e^4-12 x+8 x^2\right )}{48-64 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 23, normalized size = 1.44 \begin {gather*} \frac {15 \, {\left (16 \, x^{2} - 12 \, x + 16 \, e^{4} + 9\right )}}{4 \, {\left (4 \, x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 19, normalized size = 1.19 \begin {gather*} 15 \, x + \frac {15 \, {\left (16 \, e^{4} + 9\right )}}{4 \, {\left (4 \, x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 16, normalized size = 1.00
method | result | size |
gosper | \(\frac {60 x^{2}+60 \,{\mathrm e}^{4}}{4 x -3}\) | \(16\) |
norman | \(\frac {60 x^{2}+60 \,{\mathrm e}^{4}}{4 x -3}\) | \(19\) |
default | \(15 x -\frac {120 \left (-\frac {9}{32}-\frac {{\mathrm e}^{4}}{2}\right )}{4 x -3}\) | \(20\) |
risch | \(15 x +\frac {135}{16 \left (x -\frac {3}{4}\right )}+\frac {15 \,{\mathrm e}^{4}}{x -\frac {3}{4}}\) | \(21\) |
meijerg | \(-\frac {80 \,{\mathrm e}^{4} x}{3 \left (1-\frac {4 x}{3}\right )}+\frac {5 x \left (6-4 x \right )}{1-\frac {4 x}{3}}-\frac {30 x}{1-\frac {4 x}{3}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 19, normalized size = 1.19 \begin {gather*} 15 \, x + \frac {15 \, {\left (16 \, e^{4} + 9\right )}}{4 \, {\left (4 \, x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.16, size = 18, normalized size = 1.12 \begin {gather*} 15\,x+\frac {60\,{\mathrm {e}}^4+\frac {135}{4}}{4\,x-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 14, normalized size = 0.88 \begin {gather*} 15 x + \frac {135 + 240 e^{4}}{16 x - 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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