Optimal. Leaf size=31 \[ \frac {(3+x)^2}{x^2 \left (-\frac {126 x}{25}+3 \left (-4-e^{e^{x^2}}+x\right )\right )^2} \]
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Rubi [F]
time = 2.94, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-1125000-757500 x-191250 x^2-21250 x^3+e^{e^{x^2}} \left (-281250-93750 x+e^{x^2} \left (-562500 x^2-375000 x^3-62500 x^4\right )\right )}{9000000 x^3+140625 e^{3 e^{x^2}} x^3+4590000 x^4+780300 x^5+44217 x^6+e^{2 e^{x^2}} \left (1687500 x^3+286875 x^4\right )+e^{e^{x^2}} \left (6750000 x^3+2295000 x^4+195075 x^5\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1250 (3+x) \left (-300-75 e^{e^{x^2}}-102 x-17 x^2-50 e^{e^{x^2}+x^2} x^2 (3+x)\right )}{9 x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\\ &=\frac {1250}{9} \int \frac {(3+x) \left (-300-75 e^{e^{x^2}}-102 x-17 x^2-50 e^{e^{x^2}+x^2} x^2 (3+x)\right )}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\\ &=\frac {1250}{9} \int \left (-\frac {300 (3+x)}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3}-\frac {75 e^{e^{x^2}} (3+x)}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3}-\frac {102 (3+x)}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3}-\frac {17 (3+x)}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3}-\frac {50 e^{e^{x^2}+x^2} (3+x)^2}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx\\ &=-\left (\frac {21250}{9} \int \frac {3+x}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\right )-\frac {62500}{9} \int \frac {e^{e^{x^2}+x^2} (3+x)^2}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {31250}{3} \int \frac {e^{e^{x^2}} (3+x)}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {42500}{3} \int \frac {3+x}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {125000}{3} \int \frac {3+x}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\\ &=-\left (\frac {21250}{9} \int \left (\frac {1}{\left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {3}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx\right )-\frac {62500}{9} \int \left (\frac {6 e^{e^{x^2}+x^2}}{\left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {9 e^{e^{x^2}+x^2}}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {e^{e^{x^2}+x^2} x}{\left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx-\frac {31250}{3} \int \left (\frac {3 e^{e^{x^2}}}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {e^{e^{x^2}}}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx-\frac {42500}{3} \int \left (\frac {3}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {1}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx-\frac {125000}{3} \int \left (\frac {3}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3}+\frac {1}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3}\right ) \, dx\\ &=-\left (\frac {21250}{9} \int \frac {1}{\left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\right )-\frac {62500}{9} \int \frac {e^{e^{x^2}+x^2} x}{\left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {21250}{3} \int \frac {1}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {31250}{3} \int \frac {e^{e^{x^2}}}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {42500}{3} \int \frac {1}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-31250 \int \frac {e^{e^{x^2}}}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {125000}{3} \int \frac {e^{e^{x^2}+x^2}}{\left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-\frac {125000}{3} \int \frac {1}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-42500 \int \frac {1}{x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-62500 \int \frac {e^{e^{x^2}+x^2}}{x \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx-125000 \int \frac {1}{x^3 \left (100+25 e^{e^{x^2}}+17 x\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 28, normalized size = 0.90 \begin {gather*} \frac {625 (3+x)^2}{9 x^2 \left (100+25 e^{e^{x^2}}+17 x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 28, normalized size = 0.90
method | result | size |
risch | \(\frac {\frac {625}{9} x^{2}+\frac {1250}{3} x +625}{x^{2} \left (25 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}+17 x +100\right )^{2}}\) | \(28\) |
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. 58 vs.
\(2 (24) = 48\).
time = 0.35, size = 58, normalized size = 1.87 \begin {gather*} \frac {625 \, {\left (x^{2} + 6 \, x + 9\right )}}{9 \, {\left (289 \, x^{4} + 3400 \, x^{3} + 625 \, x^{2} e^{\left (2 \, e^{\left (x^{2}\right )}\right )} + 10000 \, x^{2} + 50 \, {\left (17 \, x^{3} + 100 \, x^{2}\right )} e^{\left (e^{\left (x^{2}\right )}\right )}\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. 58 vs.
\(2 (24) = 48\).
time = 0.41, size = 58, normalized size = 1.87 \begin {gather*} \frac {625 \, {\left (x^{2} + 6 \, x + 9\right )}}{9 \, {\left (289 \, x^{4} + 3400 \, x^{3} + 625 \, x^{2} e^{\left (2 \, e^{\left (x^{2}\right )}\right )} + 10000 \, x^{2} + 50 \, {\left (17 \, x^{3} + 100 \, x^{2}\right )} e^{\left (e^{\left (x^{2}\right )}\right )}\right )}} \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. 54 vs.
\(2 (26) = 52\).
time = 0.12, size = 54, normalized size = 1.74 \begin {gather*} \frac {625 x^{2} + 3750 x + 5625}{2601 x^{4} + 30600 x^{3} + 5625 x^{2} e^{2 e^{x^{2}}} + 90000 x^{2} + \left (7650 x^{3} + 45000 x^{2}\right ) e^{e^{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 60 vs.
\(2 (24) = 48\).
time = 0.46, size = 60, normalized size = 1.94 \begin {gather*} \frac {625 \, {\left (x^{2} + 6 \, x + 9\right )}}{9 \, {\left (289 \, x^{4} + 850 \, x^{3} e^{\left (e^{\left (x^{2}\right )}\right )} + 3400 \, x^{3} + 625 \, x^{2} e^{\left (2 \, e^{\left (x^{2}\right )}\right )} + 5000 \, x^{2} e^{\left (e^{\left (x^{2}\right )}\right )} + 10000 \, x^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {757500\,x+191250\,x^2+21250\,x^3+{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\,\left (93750\,x+{\mathrm {e}}^{x^2}\,\left (62500\,x^4+375000\,x^3+562500\,x^2\right )+281250\right )+1125000}{{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\,\left (195075\,x^5+2295000\,x^4+6750000\,x^3\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^{x^2}}\,\left (286875\,x^4+1687500\,x^3\right )+140625\,x^3\,{\mathrm {e}}^{3\,{\mathrm {e}}^{x^2}}+9000000\,x^3+4590000\,x^4+780300\,x^5+44217\,x^6} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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