Optimal. Leaf size=23 \[ 2+x+4 x \left (4+\frac {x^4}{25 \left (-25+\log \left (x^2\right )\right )^2}\right ) \]
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Rubi [A] time = 0.31, antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 11, number of rules used = 6, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {6741, 12, 6742, 2306, 2310, 2178} \begin {gather*} \frac {4 x^5}{25 \left (25-\log \left (x^2\right )\right )^2}+17 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2178
Rule 2306
Rule 2310
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6640625+516 x^4-\left (796875+20 x^4\right ) \log \left (x^2\right )+31875 \log ^2\left (x^2\right )-425 \log ^3\left (x^2\right )}{25 \left (25-\log \left (x^2\right )\right )^3} \, dx\\ &=\frac {1}{25} \int \frac {6640625+516 x^4-\left (796875+20 x^4\right ) \log \left (x^2\right )+31875 \log ^2\left (x^2\right )-425 \log ^3\left (x^2\right )}{\left (25-\log \left (x^2\right )\right )^3} \, dx\\ &=\frac {1}{25} \int \left (425-\frac {16 x^4}{\left (-25+\log \left (x^2\right )\right )^3}+\frac {20 x^4}{\left (-25+\log \left (x^2\right )\right )^2}\right ) \, dx\\ &=17 x-\frac {16}{25} \int \frac {x^4}{\left (-25+\log \left (x^2\right )\right )^3} \, dx+\frac {4}{5} \int \frac {x^4}{\left (-25+\log \left (x^2\right )\right )^2} \, dx\\ &=17 x+\frac {4 x^5}{25 \left (25-\log \left (x^2\right )\right )^2}+\frac {2 x^5}{5 \left (25-\log \left (x^2\right )\right )}-\frac {4}{5} \int \frac {x^4}{\left (-25+\log \left (x^2\right )\right )^2} \, dx+2 \int \frac {x^4}{-25+\log \left (x^2\right )} \, dx\\ &=17 x+\frac {4 x^5}{25 \left (25-\log \left (x^2\right )\right )^2}-2 \int \frac {x^4}{-25+\log \left (x^2\right )} \, dx+\frac {x^5 \operatorname {Subst}\left (\int \frac {e^{5 x/2}}{-25+x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{5/2}}\\ &=17 x+\frac {e^{125/2} x^5 \text {Ei}\left (-\frac {5}{2} \left (25-\log \left (x^2\right )\right )\right )}{\left (x^2\right )^{5/2}}+\frac {4 x^5}{25 \left (25-\log \left (x^2\right )\right )^2}-\frac {x^5 \operatorname {Subst}\left (\int \frac {e^{5 x/2}}{-25+x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{5/2}}\\ &=17 x+\frac {4 x^5}{25 \left (25-\log \left (x^2\right )\right )^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 21, normalized size = 0.91 \begin {gather*} \frac {1}{25} \left (425 x+\frac {4 x^5}{\left (-25+\log \left (x^2\right )\right )^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.49, size = 43, normalized size = 1.87 \begin {gather*} \frac {4 \, x^{5} + 425 \, x \log \left (x^{2}\right )^{2} - 21250 \, x \log \left (x^{2}\right ) + 265625 \, x}{25 \, {\left (\log \left (x^{2}\right )^{2} - 50 \, \log \left (x^{2}\right ) + 625\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 25, normalized size = 1.09 \begin {gather*} \frac {4 \, x^{5}}{25 \, {\left (\log \left (x^{2}\right )^{2} - 50 \, \log \left (x^{2}\right ) + 625\right )}} + 17 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.78
method | result | size |
risch | \(17 x +\frac {4 x^{5}}{25 \left (\ln \left (x^{2}\right )-25\right )^{2}}\) | \(18\) |
norman | \(\frac {10625 x +\frac {4 x^{5}}{25}-850 x \ln \left (x^{2}\right )+17 x \ln \left (x^{2}\right )^{2}}{\left (\ln \left (x^{2}\right )-25\right )^{2}}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 37, normalized size = 1.61 \begin {gather*} \frac {4 \, x^{5} + 1700 \, x \log \relax (x)^{2} - 42500 \, x \log \relax (x) + 265625 \, x}{25 \, {\left (4 \, \log \relax (x)^{2} - 100 \, \log \relax (x) + 625\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.74, size = 28, normalized size = 1.22 \begin {gather*} 17\,x-\frac {10625\,x-\frac {x\,\left (4\,x^4+265625\right )}{25}}{{\left (\ln \left (x^2\right )-25\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 24, normalized size = 1.04 \begin {gather*} \frac {4 x^{5}}{25 \log {\left (x^{2} \right )}^{2} - 1250 \log {\left (x^{2} \right )} + 15625} + 17 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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