Optimal. Leaf size=23 \[ 6 \left (2+x-\frac {4-\frac {x}{(5+x)^2}}{\log (x)}\right )^2 \]
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Rubi [F]
time = 0.75, 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 {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 \left (-\left ((5+x) \left (100+39 x+4 x^2\right )^2\right )+\left (25000+36750 x+22130 x^2+6914 x^3+1187 x^4+107 x^5+4 x^6\right ) \log (x)-2 x (5+x)^2 \left (245+146 x+30 x^2+2 x^3\right ) \log ^2(x)+x (2+x) (5+x)^5 \log ^3(x)\right )}{x (5+x)^5 \log ^3(x)} \, dx\\ &=12 \int \frac {-\left ((5+x) \left (100+39 x+4 x^2\right )^2\right )+\left (25000+36750 x+22130 x^2+6914 x^3+1187 x^4+107 x^5+4 x^6\right ) \log (x)-2 x (5+x)^2 \left (245+146 x+30 x^2+2 x^3\right ) \log ^2(x)+x (2+x) (5+x)^5 \log ^3(x)}{x (5+x)^5 \log ^3(x)} \, dx\\ &=12 \int \left (2+x-\frac {\left (100+39 x+4 x^2\right )^2}{x (5+x)^4 \log ^3(x)}+\frac {\left (100+39 x+4 x^2\right ) \left (250+270 x+106 x^2+17 x^3+x^4\right )}{x (5+x)^5 \log ^2(x)}-\frac {2 \left (245+146 x+30 x^2+2 x^3\right )}{(5+x)^3 \log (x)}\right ) \, dx\\ &=24 x+6 x^2-12 \int \frac {\left (100+39 x+4 x^2\right )^2}{x (5+x)^4 \log ^3(x)} \, dx+12 \int \frac {\left (100+39 x+4 x^2\right ) \left (250+270 x+106 x^2+17 x^3+x^4\right )}{x (5+x)^5 \log ^2(x)} \, dx-24 \int \frac {245+146 x+30 x^2+2 x^3}{(5+x)^3 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(23)=46\).
time = 0.05, size = 63, normalized size = 2.74 \begin {gather*} 12 \left (2 x+\frac {x^2}{2}+\frac {\left (100+39 x+4 x^2\right )^2}{2 (5+x)^4 \log ^2(x)}+\frac {-200-178 x-47 x^2-4 x^3}{(5+x)^2 \log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(92\) vs.
\(2(23)=46\).
time = 12.81, size = 93, normalized size = 4.04
method | result | size |
risch | \(6 x^{2}+24 x -\frac {6 \left (8 x^{5} \ln \left (x \right )+174 x^{4} \ln \left (x \right )-16 x^{4}+1496 x^{3} \ln \left (x \right )-312 x^{3}+6310 x^{2} \ln \left (x \right )-2321 x^{2}+12900 x \ln \left (x \right )-7800 x +10000 \ln \left (x \right )-10000\right )}{\left (5+x \right ) \left (x^{3}+15 x^{2}+75 x +125\right ) \ln \left (x \right )^{2}}\) | \(93\) |
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. 107 vs.
\(2 (21) = 42\).
time = 0.31, size = 107, normalized size = 4.65 \begin {gather*} \frac {6 \, {\left (16 \, x^{4} + 312 \, x^{3} + {\left (x^{6} + 24 \, x^{5} + 230 \, x^{4} + 1100 \, x^{3} + 2625 \, x^{2} + 2500 \, x\right )} \log \left (x\right )^{2} + 2321 \, x^{2} - 2 \, {\left (4 \, x^{5} + 87 \, x^{4} + 748 \, x^{3} + 3155 \, x^{2} + 6450 \, x + 5000\right )} \log \left (x\right ) + 7800 \, x + 10000\right )}}{{\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} \log \left (x\right )^{2}} \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. 107 vs.
\(2 (21) = 42\).
time = 0.38, size = 107, normalized size = 4.65 \begin {gather*} \frac {6 \, {\left (16 \, x^{4} + 312 \, x^{3} + {\left (x^{6} + 24 \, x^{5} + 230 \, x^{4} + 1100 \, x^{3} + 2625 \, x^{2} + 2500 \, x\right )} \log \left (x\right )^{2} + 2321 \, x^{2} - 2 \, {\left (4 \, x^{5} + 87 \, x^{4} + 748 \, x^{3} + 3155 \, x^{2} + 6450 \, x + 5000\right )} \log \left (x\right ) + 7800 \, x + 10000\right )}}{{\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} \log \left (x\right )^{2}} \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. 82 vs.
\(2 (17) = 34\).
time = 0.13, size = 82, normalized size = 3.57 \begin {gather*} 6 x^{2} + 24 x + \frac {96 x^{4} + 1872 x^{3} + 13926 x^{2} + 46800 x + \left (- 48 x^{5} - 1044 x^{4} - 8976 x^{3} - 37860 x^{2} - 77400 x - 60000\right ) \log {\left (x \right )} + 60000}{\left (x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625\right ) \log {\left (x \right )}^{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. 110 vs.
\(2 (21) = 42\).
time = 0.40, size = 110, normalized size = 4.78 \begin {gather*} 6 \, x^{2} + 24 \, x - \frac {6 \, {\left (8 \, x^{5} \log \left (x\right ) + 174 \, x^{4} \log \left (x\right ) - 16 \, x^{4} + 1496 \, x^{3} \log \left (x\right ) - 312 \, x^{3} + 6310 \, x^{2} \log \left (x\right ) - 2321 \, x^{2} + 12900 \, x \log \left (x\right ) - 7800 \, x + 10000 \, \log \left (x\right ) - 10000\right )}}{x^{4} \log \left (x\right )^{2} + 20 \, x^{3} \log \left (x\right )^{2} + 150 \, x^{2} \log \left (x\right )^{2} + 500 \, x \log \left (x\right )^{2} + 625 \, \log \left (x\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.05, size = 314, normalized size = 13.65 \begin {gather*} \frac {\frac {6\,{\left (4\,x^2+39\,x+100\right )}^2}{{\left (x+5\right )}^4}-\frac {6\,\ln \left (x\right )\,\left (4\,x^6+107\,x^5+1187\,x^4+6914\,x^3+22130\,x^2+36750\,x+25000\right )}{{\left (x+5\right )}^5}+\frac {12\,x\,{\ln \left (x\right )}^2\,\left (2\,x^3+30\,x^2+146\,x+245\right )}{{\left (x+5\right )}^3}}{{\ln \left (x\right )}^2}-480\,\ln \left (x\right )-24\,x+\frac {\frac {12\,x\,{\ln \left (x\right )}^2\,\left (2\,x^4+40\,x^3+304\,x^2+970\,x+1225\right )}{{\left (x+5\right )}^4}-\frac {6\,\left (4\,x^6+107\,x^5+1179\,x^4+6876\,x^3+22320\,x^2+37750\,x+25000\right )}{{\left (x+5\right )}^5}+\frac {12\,x\,\ln \left (x\right )\,\left (2\,x^6+60\,x^5+748\,x^4+4914\,x^3+18090\,x^2+36100\,x+31875\right )}{{\left (x+5\right )}^6}}{\ln \left (x\right )}+6\,x^2+\frac {72\,x^5+1812\,x^4+12420\,x^3+27300\,x^2}{x^6+30\,x^5+375\,x^4+2500\,x^3+9375\,x^2+18750\,x+15625}+\frac {\ln \left (x\right )\,\left (-24\,x^5+5952\,x^3+60360\,x^2+225300\,x+300000\right )}{x^4+20\,x^3+150\,x^2+500\,x+625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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