Optimal. Leaf size=18 \[ -9+x+4 x \left (-x+\frac {5 e}{3+x}\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {27, 1864}
\begin {gather*} -4 x^2+x-\frac {60 e}{x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1864
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9+60 e-66 x-47 x^2-8 x^3}{(3+x)^2} \, dx\\ &=\int \left (1-8 x+\frac {60 e}{(3+x)^2}\right ) \, dx\\ &=x-4 x^2-\frac {60 e}{3+x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.83 \begin {gather*} x-4 x^2-\frac {60 e}{3+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.30, size = 17, normalized size = 0.94
method | result | size |
default | \(-4 x^{2}+x -\frac {60 \,{\mathrm e}}{3+x}\) | \(17\) |
risch | \(-4 x^{2}+x -\frac {60 \,{\mathrm e}}{3+x}\) | \(17\) |
norman | \(\frac {-4 x^{3}-11 x^{2}-9-60 \,{\mathrm e}}{3+x}\) | \(23\) |
gosper | \(-\frac {4 x^{3}+11 x^{2}+60 \,{\mathrm e}+9}{3+x}\) | \(24\) |
meijerg | \(\frac {23 x}{1+\frac {x}{3}}+\frac {20 \,{\mathrm e} x}{3 \left (1+\frac {x}{3}\right )}+\frac {6 x \left (-\frac {2}{9} x^{2}+2 x +12\right )}{1+\frac {x}{3}}-\frac {47 x \left (x +6\right )}{3 \left (1+\frac {x}{3}\right )}\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 16, normalized size = 0.89 \begin {gather*} -4 \, x^{2} + x - \frac {60 \, e}{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 25, normalized size = 1.39 \begin {gather*} -\frac {4 \, x^{3} + 11 \, x^{2} - 3 \, x + 60 \, e}{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.78 \begin {gather*} - 4 x^{2} + x - \frac {60 e}{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 16, normalized size = 0.89 \begin {gather*} -4 \, x^{2} + x - \frac {60 \, e}{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 16, normalized size = 0.89 \begin {gather*} x-4\,x^2-\frac {60\,\mathrm {e}}{x+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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