Optimal. Leaf size=28 \[ 3 \left (-\frac {e^3}{x}+\frac {-\frac {2}{e}+\frac {x^5}{4}}{x^2}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 24, normalized size of antiderivative = 0.86, number of steps
used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14}
\begin {gather*} \frac {3 x^3}{4}-\frac {6}{e x^2}-\frac {3 e^3}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {\frac {48}{e}+12 e^3 x+9 x^5}{x^3} \, dx\\ &=\frac {1}{4} \int \left (\frac {48}{e x^3}+\frac {12 e^3}{x^2}+9 x^2\right ) \, dx\\ &=-\frac {6}{e x^2}-\frac {3 e^3}{x}+\frac {3 x^3}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 26, normalized size = 0.93 \begin {gather*} \frac {3 \left (-\frac {8}{x^2}-\frac {4 e^4}{x}+e x^3\right )}{4 e} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 24, normalized size = 0.86
method | result | size |
norman | \(\frac {\frac {3 x^{5}}{4}-6 \,{\mathrm e}^{-1}-3 x \,{\mathrm e}^{3}}{x^{2}}\) | \(22\) |
risch | \(\frac {3 x^{3}}{4}+\frac {\left (-24 \,{\mathrm e}^{-4}-12 x \right ) {\mathrm e}^{3}}{4 x^{2}}\) | \(22\) |
gosper | \(-\frac {3 \left (-x^{5}+4 x \,{\mathrm e}^{3}+4 \,{\mathrm e}^{\ln \left (2\right )-1}\right )}{4 x^{2}}\) | \(24\) |
default | \(\frac {3 x^{3}}{4}-\frac {3 \,{\mathrm e}^{3}}{x}-\frac {3 \,{\mathrm e}^{\ln \left (2\right )-1}}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 0.68 \begin {gather*} \frac {3}{4} \, x^{3} - \frac {3 \, {\left (x e^{4} + 2\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 36, normalized size = 1.29 \begin {gather*} \frac {3 \, {\left (x^{5} e^{\left (3 \, \log \left (2\right ) - 3\right )} - 32 \, x - 4 \, e^{\left (4 \, \log \left (2\right ) - 4\right )}\right )} e^{\left (-3 \, \log \left (2\right ) + 3\right )}}{4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 26, normalized size = 0.93 \begin {gather*} \frac {3 e x^{3} + \frac {- 12 x e^{4} - 24}{x^{2}}}{4 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 21, normalized size = 0.75 \begin {gather*} \frac {3}{4} \, x^{3} - \frac {3 \, {\left (x e^{3} + e^{\left (\log \left (2\right ) - 1\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 20, normalized size = 0.71 \begin {gather*} \frac {3\,x^3}{4}-\frac {{\mathrm {e}}^{-1}\,\left (3\,x\,{\mathrm {e}}^4+6\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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