Optimal. Leaf size=27 \[ \frac {25+\frac {e^{10}}{(1-2 x)^2 (5-x)^2}-x}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(27)=54\).
time = 0.20, antiderivative size = 69, normalized size of antiderivative = 2.56, number of steps
used = 2, number of rules used = 1, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2099}
\begin {gather*} \frac {29 e^{10}}{18225 (5-x)}+\frac {625+e^{10}}{25 x}+\frac {e^{10}}{405 (5-x)^2}+\frac {56 e^{10}}{729 (1-2 x)}+\frac {8 e^{10}}{81 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 e^{10}}{405 (-5+x)^3}+\frac {29 e^{10}}{18225 (-5+x)^2}+\frac {-625-e^{10}}{25 x^2}-\frac {32 e^{10}}{81 (-1+2 x)^3}+\frac {112 e^{10}}{729 (-1+2 x)^2}\right ) \, dx\\ &=\frac {8 e^{10}}{81 (1-2 x)^2}+\frac {56 e^{10}}{729 (1-2 x)}+\frac {e^{10}}{405 (5-x)^2}+\frac {29 e^{10}}{18225 (5-x)}+\frac {625+e^{10}}{25 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 34, normalized size = 1.26 \begin {gather*} \frac {e^{10}+25 \left (5-11 x+2 x^2\right )^2}{x \left (5-11 x+2 x^2\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 53, normalized size = 1.96
method | result | size |
norman | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (2 x^{2}-11 x +5\right )^{2}}\) | \(41\) |
gosper | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (4 x^{4}-44 x^{3}+141 x^{2}-110 x +25\right )}\) | \(51\) |
risch | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (4 x^{4}-44 x^{3}+141 x^{2}-110 x +25\right )}\) | \(52\) |
default | \(\frac {{\mathrm e}^{10}}{405 \left (x -5\right )^{2}}-\frac {29 \,{\mathrm e}^{10}}{18225 \left (x -5\right )}-\frac {-\frac {{\mathrm e}^{10}}{25}-25}{x}+\frac {8 \,{\mathrm e}^{10}}{81 \left (2 x -1\right )^{2}}-\frac {56 \,{\mathrm e}^{10}}{729 \left (2 x -1\right )}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 49 vs.
\(2 (24) = 48\).
time = 0.25, size = 49, normalized size = 1.81 \begin {gather*} \frac {100 \, x^{4} - 1100 \, x^{3} + 3525 \, x^{2} - 2750 \, x + e^{10} + 625}{4 \, x^{5} - 44 \, x^{4} + 141 \, x^{3} - 110 \, x^{2} + 25 \, x} \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. 49 vs.
\(2 (24) = 48\).
time = 0.35, size = 49, normalized size = 1.81 \begin {gather*} \frac {100 \, x^{4} - 1100 \, x^{3} + 3525 \, x^{2} - 2750 \, x + e^{10} + 625}{4 \, x^{5} - 44 \, x^{4} + 141 \, x^{3} - 110 \, x^{2} + 25 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (19) = 38\).
time = 0.51, size = 48, normalized size = 1.78 \begin {gather*} - \frac {- 100 x^{4} + 1100 x^{3} - 3525 x^{2} + 2750 x - e^{10} - 625}{4 x^{5} - 44 x^{4} + 141 x^{3} - 110 x^{2} + 25 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 48, normalized size = 1.78 \begin {gather*} \frac {e^{10} + 625}{25 \, x} - \frac {4 \, x^{3} e^{10} - 44 \, x^{2} e^{10} + 141 \, x e^{10} - 110 \, e^{10}}{25 \, {\left (2 \, x^{2} - 11 \, x + 5\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.39, size = 53, normalized size = 1.96 \begin {gather*} \frac {8\,{\mathrm {e}}^{10}}{81\,{\left (2\,x-1\right )}^2}-\frac {56\,{\mathrm {e}}^{10}}{729\,\left (2\,x-1\right )}+\frac {\frac {{\mathrm {e}}^{10}}{25}+25}{x}-\frac {29\,{\mathrm {e}}^{10}}{18225\,\left (x-5\right )}+\frac {{\mathrm {e}}^{10}}{405\,{\left (x-5\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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