Optimal. Leaf size=12 \[ \frac {750}{(4-e)^2 x^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {6, 12, 30}
\begin {gather*} \frac {750}{(4-e)^2 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int -\frac {2250}{(16-8 e) x^4+e^2 x^4} \, dx\\ &=\int -\frac {2250}{\left (16-8 e+e^2\right ) x^4} \, dx\\ &=-\frac {2250 \int \frac {1}{x^4} \, dx}{(4-e)^2}\\ &=\frac {750}{(4-e)^2 x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} \frac {750}{(-4+e)^2 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 18, normalized size = 1.50
method | result | size |
norman | \(\frac {750}{\left ({\mathrm e}-4\right )^{2} x^{3}}\) | \(12\) |
risch | \(\frac {750}{x^{3} \left (-8 \,{\mathrm e}+16+{\mathrm e}^{2}\right )}\) | \(16\) |
gosper | \(\frac {750}{x^{3} \left (-8 \,{\mathrm e}+16+{\mathrm e}^{2}\right )}\) | \(18\) |
default | \(\frac {750}{x^{3} \left (-8 \,{\mathrm e}+16+{\mathrm e}^{2}\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 15, normalized size = 1.25 \begin {gather*} \frac {750}{x^{3} {\left (e^{2} - 8 \, e + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 23 vs.
\(2 (11) = 22\).
time = 0.35, size = 23, normalized size = 1.92 \begin {gather*} \frac {750}{x^{3} e^{2} - 8 \, x^{3} e + 16 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 1.17 \begin {gather*} \frac {750}{x^{3} \left (- 8 e + e^{2} + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 1.25 \begin {gather*} \frac {750}{x^{3} {\left (e^{2} - 8 \, e + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 11, normalized size = 0.92 \begin {gather*} \frac {750}{x^3\,{\left (\mathrm {e}-4\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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