3.53.8 \(\int \frac {1250 x^2-2500 x^3+1250 x^4+(625 x^2-2500 x^3+1875 x^4) \log (\frac {6}{5 x^2})+(-2000 x^2+2000 x^3) \log (\frac {6}{5 x^2}) \log (x^2)+(-1000 x^2+1000 x^3+(-500 x^2+1000 x^3) \log (\frac {6}{5 x^2})) \log ^2(x^2)+(-400 x+1200 x^2) \log (\frac {6}{5 x^2}) \log ^3(x^2)+(-100 x+300 x^2+150 x^2 \log (\frac {6}{5 x^2})) \log ^4(x^2)+240 x \log (\frac {6}{5 x^2}) \log ^5(x^2)+40 x \log ^6(x^2)+16 \log (\frac {6}{5 x^2}) \log ^7(x^2)+(2-\log (\frac {6}{5 x^2})) \log ^8(x^2)}{625 x^2 \log ^2(\frac {6}{5 x^2})} \, dx\)

Optimal. Leaf size=34 \[ \frac {\left (x-\left (x+\frac {1}{5} \log ^2\left (x^2\right )\right )^2\right )^2}{x \log \left (\frac {6}{5 x^2}\right )} \]

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Rubi [F]  time = 2.37, 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 {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{625 x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1250*x^2 - 2500*x^3 + 1250*x^4 + (625*x^2 - 2500*x^3 + 1875*x^4)*Log[6/(5*x^2)] + (-2000*x^2 + 2000*x^3)*
Log[6/(5*x^2)]*Log[x^2] + (-1000*x^2 + 1000*x^3 + (-500*x^2 + 1000*x^3)*Log[6/(5*x^2)])*Log[x^2]^2 + (-400*x +
1200*x^2)*Log[6/(5*x^2)]*Log[x^2]^3 + (-100*x + 300*x^2 + 150*x^2*Log[6/(5*x^2)])*Log[x^2]^4 + 240*x*Log[6/(5
*x^2)]*Log[x^2]^5 + 40*x*Log[x^2]^6 + 16*Log[6/(5*x^2)]*Log[x^2]^7 + (2 - Log[6/(5*x^2)])*Log[x^2]^8)/(625*x^2
*Log[6/(5*x^2)]^2),x]

[Out]

(16*x)/5 - (8*x^2)/5 + ((1 - x)^2*x)/Log[6/(5*x^2)] - (48*ExpIntegralEi[-Log[6/(5*x^2)]]*Log[6/(5*x^2)])/25 +
(8*Sqrt[6/5]*Sqrt[x^(-2)]*x*ExpIntegralEi[-1/2*Log[6/(5*x^2)]]*Log[6/(5*x^2)])/5 - (48*ExpIntegralEi[-Log[6/(5
*x^2)]]*Log[x^2])/25 + (8*Sqrt[6/5]*Sqrt[x^(-2)]*x*ExpIntegralEi[-1/2*Log[6/(5*x^2)]]*Log[x^2])/5 - (8*Defer[I
nt][Log[x^2]^2/Log[6/(5*x^2)]^2, x])/5 + (8*Defer[Int][(x*Log[x^2]^2)/Log[6/(5*x^2)]^2, x])/5 - (4*Defer[Int][
Log[x^2]^2/Log[6/(5*x^2)], x])/5 + (8*Defer[Int][(x*Log[x^2]^2)/Log[6/(5*x^2)], x])/5 + (48*Defer[Int][Log[x^2
]^3/Log[6/(5*x^2)], x])/25 - (16*Defer[Int][Log[x^2]^3/(x*Log[6/(5*x^2)]), x])/25 + (12*Defer[Int][Log[x^2]^4/
Log[6/(5*x^2)]^2, x])/25 - (4*Defer[Int][Log[x^2]^4/(x*Log[6/(5*x^2)]^2), x])/25 + (6*Defer[Int][Log[x^2]^4/Lo
g[6/(5*x^2)], x])/25 + (48*Defer[Int][Log[x^2]^5/(x*Log[6/(5*x^2)]), x])/125 + (8*Defer[Int][Log[x^2]^6/(x*Log
[6/(5*x^2)]^2), x])/125 + (16*Defer[Int][Log[x^2]^7/(x^2*Log[6/(5*x^2)]), x])/625 + (2*Defer[Int][Log[x^2]^8/(
x^2*Log[6/(5*x^2)]^2), x])/625 - Defer[Int][Log[x^2]^8/(x^2*Log[6/(5*x^2)]), x]/625

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \frac {1250 x^2-2500 x^3+1250 x^4+\left (625 x^2-2500 x^3+1875 x^4\right ) \log \left (\frac {6}{5 x^2}\right )+\left (-2000 x^2+2000 x^3\right ) \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right )+\left (-1000 x^2+1000 x^3+\left (-500 x^2+1000 x^3\right ) \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )+\left (-400 x+1200 x^2\right ) \log \left (\frac {6}{5 x^2}\right ) \log ^3\left (x^2\right )+\left (-100 x+300 x^2+150 x^2 \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )+240 x \log \left (\frac {6}{5 x^2}\right ) \log ^5\left (x^2\right )+40 x \log ^6\left (x^2\right )+16 \log \left (\frac {6}{5 x^2}\right ) \log ^7\left (x^2\right )+\left (2-\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=\frac {1}{625} \int \frac {\left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right ) \left (\log \left (\frac {6}{5 x^2}\right ) \left (25 x (-1+3 x)+80 x \log \left (x^2\right )+10 x \log ^2\left (x^2\right )+16 \log ^3\left (x^2\right )-\log ^4\left (x^2\right )\right )+2 \left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right )\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=\frac {1}{625} \int \left (\frac {625 (-1+x) \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+3 x \log \left (\frac {6}{5 x^2}\right )\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {2000 (-1+x) \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {500 \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+2 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {400 (-1+3 x) \log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {50 \left (-2+6 x+3 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {240 \log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}+\frac {40 \log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {16 \log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}-\frac {\left (-2+\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}\right ) \, dx\\ &=-\left (\frac {1}{625} \int \frac {\left (-2+\log \left (\frac {6}{5 x^2}\right )\right ) \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx\right )+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {2}{25} \int \frac {\left (-2+6 x+3 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{25} \int \frac {(-1+3 x) \log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {4}{5} \int \frac {\left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+2 x \log \left (\frac {6}{5 x^2}\right )\right ) \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{5} \int \frac {(-1+x) \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\int \frac {(-1+x) \left (-2+2 x-\log \left (\frac {6}{5 x^2}\right )+3 x \log \left (\frac {6}{5 x^2}\right )\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx\\ &=-\left (\frac {1}{625} \int \left (-\frac {2 \log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {\log ^8\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )}\right ) \, dx\right )+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {2}{25} \int \left (\frac {6 \log ^4\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}-\frac {2 \log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )}+\frac {3 \log ^4\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{25} \int \left (\frac {3 \log ^3\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}-\frac {\log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {4}{5} \int \left (-\frac {2 \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {2 x \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )}-\frac {\log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {2 x \log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\frac {16}{5} \int \left (-\frac {\log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}+\frac {x \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx+\int \left (\frac {2 (-1+x)^2}{\log ^2\left (\frac {6}{5 x^2}\right )}+\frac {1-4 x+3 x^2}{\log \left (\frac {6}{5 x^2}\right )}\right ) \, dx\\ &=-\left (\frac {1}{625} \int \frac {\log ^8\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx\right )+\frac {2}{625} \int \frac {\log ^8\left (x^2\right )}{x^2 \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{625} \int \frac {\log ^7\left (x^2\right )}{x^2 \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{125} \int \frac {\log ^6\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {4}{25} \int \frac {\log ^4\left (x^2\right )}{x \log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {6}{25} \int \frac {\log ^4\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{125} \int \frac {\log ^5\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {12}{25} \int \frac {\log ^4\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {16}{25} \int \frac {\log ^3\left (x^2\right )}{x \log \left (\frac {6}{5 x^2}\right )} \, dx-\frac {4}{5} \int \frac {\log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx-\frac {8}{5} \int \frac {\log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{5} \int \frac {x \log ^2\left (x^2\right )}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx+\frac {8}{5} \int \frac {x \log ^2\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {48}{25} \int \frac {\log ^3\left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+2 \int \frac {(-1+x)^2}{\log ^2\left (\frac {6}{5 x^2}\right )} \, dx-\frac {16}{5} \int \frac {\log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\frac {16}{5} \int \frac {x \log \left (x^2\right )}{\log \left (\frac {6}{5 x^2}\right )} \, dx+\int \frac {1-4 x+3 x^2}{\log \left (\frac {6}{5 x^2}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.16, size = 204, normalized size = 6.00 \begin {gather*} \frac {1}{625} \left (-180 \log ^5\left (\frac {6}{5 x^2}\right )-600 \log ^4\left (\frac {6}{5 x^2}\right ) \left (\log (x)+\log \left (x^2\right )\right )-600 \log ^2\left (\frac {6}{5 x^2}\right ) \log (x) \left (-1+6 \log ^2\left (x^2\right )\right )-100 \log ^3\left (\frac {6}{5 x^2}\right ) \left (-1+24 \log (x) \log \left (x^2\right )+6 \log ^2\left (x^2\right )\right )+\frac {\left (25 (-1+x) x+10 x \log ^2\left (x^2\right )+\log ^4\left (x^2\right )\right )^2}{x \log \left (\frac {6}{5 x^2}\right )}-40 \log ^2\left (x^2\right ) \left (5 \log \left (x^2\right )-3 \log ^3\left (x^2\right )+15 \log (x) \left (-1+\log ^2\left (x^2\right )\right )\right )+300 \log \left (\frac {6}{5 x^2}\right ) \log \left (x^2\right ) \left (\log (x) \left (4-8 \log ^2\left (x^2\right )\right )+\log \left (x^2\right ) \left (-1+\log ^2\left (x^2\right )\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1250*x^2 - 2500*x^3 + 1250*x^4 + (625*x^2 - 2500*x^3 + 1875*x^4)*Log[6/(5*x^2)] + (-2000*x^2 + 2000
*x^3)*Log[6/(5*x^2)]*Log[x^2] + (-1000*x^2 + 1000*x^3 + (-500*x^2 + 1000*x^3)*Log[6/(5*x^2)])*Log[x^2]^2 + (-4
00*x + 1200*x^2)*Log[6/(5*x^2)]*Log[x^2]^3 + (-100*x + 300*x^2 + 150*x^2*Log[6/(5*x^2)])*Log[x^2]^4 + 240*x*Lo
g[6/(5*x^2)]*Log[x^2]^5 + 40*x*Log[x^2]^6 + 16*Log[6/(5*x^2)]*Log[x^2]^7 + (2 - Log[6/(5*x^2)])*Log[x^2]^8)/(6
25*x^2*Log[6/(5*x^2)]^2),x]

[Out]

(-180*Log[6/(5*x^2)]^5 - 600*Log[6/(5*x^2)]^4*(Log[x] + Log[x^2]) - 600*Log[6/(5*x^2)]^2*Log[x]*(-1 + 6*Log[x^
2]^2) - 100*Log[6/(5*x^2)]^3*(-1 + 24*Log[x]*Log[x^2] + 6*Log[x^2]^2) + (25*(-1 + x)*x + 10*x*Log[x^2]^2 + Log
[x^2]^4)^2/(x*Log[6/(5*x^2)]) - 40*Log[x^2]^2*(5*Log[x^2] - 3*Log[x^2]^3 + 15*Log[x]*(-1 + Log[x^2]^2)) + 300*
Log[6/(5*x^2)]*Log[x^2]*(Log[x]*(4 - 8*Log[x^2]^2) + Log[x^2]*(-1 + Log[x^2]^2)))/625

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fricas [B]  time = 0.54, size = 285, normalized size = 8.38 \begin {gather*} \frac {\log \left (\frac {6}{5}\right )^{8} - 8 \, \log \left (\frac {6}{5}\right ) \log \left (\frac {6}{5 \, x^{2}}\right )^{7} + \log \left (\frac {6}{5 \, x^{2}}\right )^{8} + 20 \, x \log \left (\frac {6}{5}\right )^{6} + 4 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{2} + 5 \, x\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{6} - 8 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{3} + 15 \, x \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{5} + 50 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )^{4} + 10 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{4} + 30 \, x \log \left (\frac {6}{5}\right )^{2} + 15 \, x^{2} - 5 \, x\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{4} + 625 \, x^{4} - 8 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{5} + 50 \, x \log \left (\frac {6}{5}\right )^{3} + 25 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{3} - 1250 \, x^{3} + 500 \, {\left (x^{3} - x^{2}\right )} \log \left (\frac {6}{5}\right )^{2} + 4 \, {\left (7 \, \log \left (\frac {6}{5}\right )^{6} + 75 \, x \log \left (\frac {6}{5}\right )^{4} + 125 \, x^{3} + 75 \, {\left (3 \, x^{2} - x\right )} \log \left (\frac {6}{5}\right )^{2} - 125 \, x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )^{2} + 625 \, x^{2} - 8 \, {\left (\log \left (\frac {6}{5}\right )^{7} + 75 \, x^{2} \log \left (\frac {6}{5}\right )^{3} + 125 \, {\left (x^{3} - x^{2}\right )} \log \left (\frac {6}{5}\right )\right )} \log \left (\frac {6}{5 \, x^{2}}\right )}{625 \, x \log \left (\frac {6}{5 \, x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+40*x*log(x^2)^6+240*x*log(6/5/x^2)*lo
g(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2-100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-5
00*x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6/5/x^2)*log(x^2)+(1875*x^4-2500*x^
3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="fricas")

[Out]

1/625*(log(6/5)^8 - 8*log(6/5)*log(6/5/x^2)^7 + log(6/5/x^2)^8 + 20*x*log(6/5)^6 + 4*(7*log(6/5)^2 + 5*x)*log(
6/5/x^2)^6 - 8*(7*log(6/5)^3 + 15*x*log(6/5))*log(6/5/x^2)^5 + 50*(3*x^2 - x)*log(6/5)^4 + 10*(7*log(6/5)^4 +
30*x*log(6/5)^2 + 15*x^2 - 5*x)*log(6/5/x^2)^4 + 625*x^4 - 8*(7*log(6/5)^5 + 50*x*log(6/5)^3 + 25*(3*x^2 - x)*
log(6/5))*log(6/5/x^2)^3 - 1250*x^3 + 500*(x^3 - x^2)*log(6/5)^2 + 4*(7*log(6/5)^6 + 75*x*log(6/5)^4 + 125*x^3
+ 75*(3*x^2 - x)*log(6/5)^2 - 125*x^2)*log(6/5/x^2)^2 + 625*x^2 - 8*(log(6/5)^7 + 75*x^2*log(6/5)^3 + 125*(x^
3 - x^2)*log(6/5))*log(6/5/x^2))/(x*log(6/5/x^2))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (\log \left (\frac {6}{5 \, x^{2}}\right ) - 2\right )} \log \left (x^{2}\right )^{8} - 16 \, \log \left (x^{2}\right )^{7} \log \left (\frac {6}{5 \, x^{2}}\right ) - 40 \, x \log \left (x^{2}\right )^{6} - 240 \, x \log \left (x^{2}\right )^{5} \log \left (\frac {6}{5 \, x^{2}}\right ) - 50 \, {\left (3 \, x^{2} \log \left (\frac {6}{5 \, x^{2}}\right ) + 6 \, x^{2} - 2 \, x\right )} \log \left (x^{2}\right )^{4} - 400 \, {\left (3 \, x^{2} - x\right )} \log \left (x^{2}\right )^{3} \log \left (\frac {6}{5 \, x^{2}}\right ) - 1250 \, x^{4} + 2500 \, x^{3} - 500 \, {\left (2 \, x^{3} - 2 \, x^{2} + {\left (2 \, x^{3} - x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )\right )} \log \left (x^{2}\right )^{2} - 2000 \, {\left (x^{3} - x^{2}\right )} \log \left (x^{2}\right ) \log \left (\frac {6}{5 \, x^{2}}\right ) - 1250 \, x^{2} - 625 \, {\left (3 \, x^{4} - 4 \, x^{3} + x^{2}\right )} \log \left (\frac {6}{5 \, x^{2}}\right )}{625 \, x^{2} \log \left (\frac {6}{5 \, x^{2}}\right )^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+40*x*log(x^2)^6+240*x*log(6/5/x^2)*lo
g(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2-100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-5
00*x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6/5/x^2)*log(x^2)+(1875*x^4-2500*x^
3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="giac")

[Out]

integrate(-1/625*((log(6/5/x^2) - 2)*log(x^2)^8 - 16*log(x^2)^7*log(6/5/x^2) - 40*x*log(x^2)^6 - 240*x*log(x^2
)^5*log(6/5/x^2) - 50*(3*x^2*log(6/5/x^2) + 6*x^2 - 2*x)*log(x^2)^4 - 400*(3*x^2 - x)*log(x^2)^3*log(6/5/x^2)
- 1250*x^4 + 2500*x^3 - 500*(2*x^3 - 2*x^2 + (2*x^3 - x^2)*log(6/5/x^2))*log(x^2)^2 - 2000*(x^3 - x^2)*log(x^2
)*log(6/5/x^2) - 1250*x^2 - 625*(3*x^4 - 4*x^3 + x^2)*log(6/5/x^2))/(x^2*log(6/5/x^2)^2), x)

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maple [C]  time = 30.42, size = 35897, normalized size = 1055.79

method	result	size
risch	\(\text {Expression too large to display}\)	\(35897\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/625*((-ln(6/5/x^2)+2)*ln(x^2)^8+16*ln(6/5/x^2)*ln(x^2)^7+40*x*ln(x^2)^6+240*x*ln(6/5/x^2)*ln(x^2)^5+(150
*x^2*ln(6/5/x^2)+300*x^2-100*x)*ln(x^2)^4+(1200*x^2-400*x)*ln(6/5/x^2)*ln(x^2)^3+((1000*x^3-500*x^2)*ln(6/5/x^
2)+1000*x^3-1000*x^2)*ln(x^2)^2+(2000*x^3-2000*x^2)*ln(6/5/x^2)*ln(x^2)+(1875*x^4-2500*x^3+625*x^2)*ln(6/5/x^2
)+1250*x^4-2500*x^3+1250*x^2)/x^2/ln(6/5/x^2)^2,x,method=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [B]  time = 0.49, size = 627, normalized size = 18.44 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((-log(6/5/x^2)+2)*log(x^2)^8+16*log(6/5/x^2)*log(x^2)^7+40*x*log(x^2)^6+240*x*log(6/5/x^2)*lo
g(x^2)^5+(150*x^2*log(6/5/x^2)+300*x^2-100*x)*log(x^2)^4+(1200*x^2-400*x)*log(6/5/x^2)*log(x^2)^3+((1000*x^3-5
00*x^2)*log(6/5/x^2)+1000*x^3-1000*x^2)*log(x^2)^2+(2000*x^3-2000*x^2)*log(6/5/x^2)*log(x^2)+(1875*x^4-2500*x^
3+625*x^2)*log(6/5/x^2)+1250*x^4-2500*x^3+1250*x^2)/x^2/log(6/5/x^2)^2,x, algorithm="maxima")

[Out]

-1/625*(256*log(x)^8 + 1280*x*log(x)^6 + 800*(3*x^2 - x)*log(x)^4 + 625*x^4 - 1250*x^3 + 20*(2*log(5)^5 + 10*l
og(5)*log(3)^4 - 2*log(3)^5 + 10*(log(5) - log(3))*log(2)^4 - 2*log(2)^5 - 5*(4*log(5)^2 - 1)*log(3)^3 - 5*(4*
log(5)^2 - 8*log(5)*log(3) + 4*log(3)^2 - 1)*log(2)^3 - 5*log(5)^3 + 5*(4*log(5)^3 - 3*log(5))*log(3)^2 + 5*(4
*log(5)^3 + 12*log(5)*log(3)^2 - 4*log(3)^3 - 3*(4*log(5)^2 - 1)*log(3) - 3*log(5))*log(2)^2 - 5*(2*log(5)^4 -
3*log(5)^2)*log(3) - 5*(2*log(5)^4 - 8*log(5)*log(3)^3 + 2*log(3)^4 + 3*(4*log(5)^2 - 1)*log(3)^2 - 3*log(5)^
2 - 2*(4*log(5)^3 - 3*log(5))*log(3))*log(2))*x*log(x) + 2000*(x^3 - x^2)*log(x)^2 + 10*(2*log(5)^6 - 12*log(5
)*log(3)^5 + 2*log(3)^6 - 12*(log(5) - log(3))*log(2)^5 + 2*log(2)^6 + 5*(6*log(5)^2 - 1)*log(3)^4 + 5*(6*log(
5)^2 - 12*log(5)*log(3) + 6*log(3)^2 - 1)*log(2)^4 - 5*log(5)^4 - 20*(2*log(5)^3 - log(5))*log(3)^3 - 20*(2*lo
g(5)^3 + 6*log(5)*log(3)^2 - 2*log(3)^3 - (6*log(5)^2 - 1)*log(3) - log(5))*log(2)^3 + 30*(log(5)^4 - log(5)^2
)*log(3)^2 + 30*(log(5)^4 - 4*log(5)*log(3)^3 + log(3)^4 + (6*log(5)^2 - 1)*log(3)^2 - log(5)^2 - 2*(2*log(5)^
3 - log(5))*log(3))*log(2)^2 - 4*(3*log(5)^5 - 5*log(5)^3)*log(3) - 4*(3*log(5)^5 + 15*log(5)*log(3)^4 - 3*log
(3)^5 - 5*(6*log(5)^2 - 1)*log(3)^3 - 5*log(5)^3 + 15*(2*log(5)^3 - log(5))*log(3)^2 - 15*(log(5)^4 - log(5)^2
)*log(3))*log(2))*x + 625*x^2)/(x*(log(5) - log(3) - log(2)) + 2*x*log(x))

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mupad [B]  time = 4.11, size = 520, normalized size = 15.29 \begin {gather*} -\frac {\frac {1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^2-500\,x^2\,{\ln \left (\frac {6}{5}\right )}^3-1000\,x^2\,{\ln \left (\frac {6}{5}\right )}^2+300\,x^2\,{\ln \left (\frac {6}{5}\right )}^4+1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^3+150\,x^2\,{\ln \left (\frac {6}{5}\right )}^5+625\,x^2\,\ln \left (\frac {6}{5}\right )-2500\,x^3\,\ln \left (\frac {6}{5}\right )-100\,x\,{\ln \left (\frac {6}{5}\right )}^4+1875\,x^4\,\ln \left (\frac {6}{5}\right )+40\,x\,{\ln \left (\frac {6}{5}\right )}^6+2\,{\ln \left (\frac {6}{5}\right )}^8-{\ln \left (\frac {6}{5}\right )}^9+1250\,x^2-2500\,x^3+1250\,x^4}{1250\,x}-\frac {\ln \left (x^2\right )\,\left (1000\,x^3\,{\ln \left (\frac {6}{5}\right )}^2-500\,x^2\,{\ln \left (\frac {6}{5}\right )}^2+150\,x^2\,{\ln \left (\frac {6}{5}\right )}^4-{\ln \left (\frac {6}{5}\right )}^8+625\,x^2-2500\,x^3+1875\,x^4\right )}{1250\,x}}{\ln \left (x^2\right )-\ln \left (\frac {6}{5}\right )}-{\ln \left (x^2\right )}^2\,\left (\frac {182\,\ln \left (\frac {6}{5}\right )}{125}+\frac {\frac {6\,\ln \left (\frac {6}{5}\right )\,x^2}{25}+\left (-\frac {192\,\ln \left (\frac {6}{5}\right )}{125}-\frac {24\,{\ln \left (\frac {6}{5}\right )}^2}{125}-\frac {372}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^5}{625}}{x}+\frac {24\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^3}{125}+\frac {372}{25}\right )-{\ln \left (x^2\right )}^3\,\left (\frac {32\,\ln \left (\frac {6}{5}\right )}{125}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {\frac {6\,x^2}{25}+\left (-\frac {32\,\ln \left (\frac {6}{5}\right )}{125}-\frac {64}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^4}{625}}{x}+\frac {62}{25}\right )-{\ln \left (x^2\right )}^5\,\left (\frac {{\ln \left (\frac {6}{5}\right )}^2}{625\,x}+\frac {4}{125}\right )-x\,\left (\frac {6\,{\ln \left (\frac {6}{5}\right )}^3}{25}-\frac {2\,{\ln \left (\frac {6}{5}\right )}^2}{5}-\frac {4\,\ln \left (\frac {6}{5}\right )}{5}+\frac {3\,{\ln \left (\frac {6}{5}\right )}^4}{25}+\frac {1}{2}\right )-x^2\,\left (\frac {4\,\ln \left (\frac {6}{5}\right )}{5}+\frac {4\,{\ln \left (\frac {6}{5}\right )}^2}{5}-2\right )-{\ln \left (x^2\right )}^4\,\left (\frac {4\,\ln \left (\frac {6}{5}\right )}{125}-\frac {\frac {8\,x}{25}-\frac {{\ln \left (\frac {6}{5}\right )}^3}{625}}{x}+\frac {8}{25}\right )-\frac {3\,x^3}{2}-\frac {{\ln \left (x^2\right )}^7}{625\,x}-\frac {\frac {{\ln \left (\frac {6}{5}\right )}^7}{625}-\frac {{\ln \left (\frac {6}{5}\right )}^8}{1250}}{x}-\ln \relax (x)\,\left (\frac {1456\,\ln \left (\frac {6}{5}\right )}{125}+\frac {172\,{\ln \left (\frac {6}{5}\right )}^2}{125}+\frac {32\,{\ln \left (\frac {6}{5}\right )}^3}{125}+\frac {8\,{\ln \left (\frac {6}{5}\right )}^4}{125}+\frac {2976}{25}\right )-\frac {{\ln \left (x^2\right )}^6\,\ln \left (\frac {6}{5}\right )}{625\,x}-\frac {\ln \left (x^2\right )\,\left (\frac {4\,x^3}{5}+\left (\frac {6\,{\ln \left (\frac {6}{5}\right )}^2}{25}-\frac {4}{5}\right )\,x^2+\left (-\frac {728\,\ln \left (\frac {6}{5}\right )}{125}-\frac {96\,{\ln \left (\frac {6}{5}\right )}^2}{125}-\frac {16\,{\ln \left (\frac {6}{5}\right )}^3}{125}-\frac {1488}{25}\right )\,x+\frac {{\ln \left (\frac {6}{5}\right )}^6}{625}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((log(6/(5*x^2))*(625*x^2 - 2500*x^3 + 1875*x^4))/625 - (log(x^2)^8*(log(6/(5*x^2)) - 2))/625 + (log(x^2)^
4*(300*x^2 - 100*x + 150*x^2*log(6/(5*x^2))))/625 + (8*x*log(x^2)^6)/125 - (log(x^2)^2*(log(6/(5*x^2))*(500*x^
2 - 1000*x^3) + 1000*x^2 - 1000*x^3))/625 + (16*log(x^2)^7*log(6/(5*x^2)))/625 + 2*x^2 - 4*x^3 + 2*x^4 - (log(
x^2)^3*log(6/(5*x^2))*(400*x - 1200*x^2))/625 - (log(x^2)*log(6/(5*x^2))*(2000*x^2 - 2000*x^3))/625 + (48*x*lo
g(x^2)^5*log(6/(5*x^2)))/125)/(x^2*log(6/(5*x^2))^2),x)

[Out]

- ((1000*x^3*log(6/5)^2 - 500*x^2*log(6/5)^3 - 1000*x^2*log(6/5)^2 + 300*x^2*log(6/5)^4 + 1000*x^3*log(6/5)^3
+ 150*x^2*log(6/5)^5 + 625*x^2*log(6/5) - 2500*x^3*log(6/5) - 100*x*log(6/5)^4 + 1875*x^4*log(6/5) + 40*x*log(
6/5)^6 + 2*log(6/5)^8 - log(6/5)^9 + 1250*x^2 - 2500*x^3 + 1250*x^4)/(1250*x) - (log(x^2)*(1000*x^3*log(6/5)^2
- 500*x^2*log(6/5)^2 + 150*x^2*log(6/5)^4 - log(6/5)^8 + 625*x^2 - 2500*x^3 + 1875*x^4))/(1250*x))/(log(x^2)
- log(6/5)) - log(x^2)^2*((182*log(6/5))/125 + ((6*x^2*log(6/5))/25 - x*((192*log(6/5))/125 + (24*log(6/5)^2)/
125 + 372/25) + log(6/5)^5/625)/x + (24*log(6/5)^2)/125 + (4*log(6/5)^3)/125 + 372/25) - log(x^2)^3*((32*log(6
/5))/125 + (4*log(6/5)^2)/125 + (log(6/5)^4/625 - x*((32*log(6/5))/125 + 64/25) + (6*x^2)/25)/x + 62/25) - log
(x^2)^5*(log(6/5)^2/(625*x) + 4/125) - x*((6*log(6/5)^3)/25 - (2*log(6/5)^2)/5 - (4*log(6/5))/5 + (3*log(6/5)^
4)/25 + 1/2) - x^2*((4*log(6/5))/5 + (4*log(6/5)^2)/5 - 2) - log(x^2)^4*((4*log(6/5))/125 - ((8*x)/25 - log(6/
5)^3/625)/x + 8/25) - (3*x^3)/2 - log(x^2)^7/(625*x) - (log(6/5)^7/625 - log(6/5)^8/1250)/x - log(x)*((1456*lo
g(6/5))/125 + (172*log(6/5)^2)/125 + (32*log(6/5)^3)/125 + (8*log(6/5)^4)/125 + 2976/25) - (log(x^2)^6*log(6/5
))/(625*x) - (log(x^2)*(x^2*((6*log(6/5)^2)/25 - 4/5) - x*((728*log(6/5))/125 + (96*log(6/5)^2)/125 + (16*log(
6/5)^3)/125 + 1488/25) + log(6/5)^6/625 + (4*x^3)/5))/x

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sympy [B]  time = 4.43, size = 1028, normalized size = 30.24 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((-ln(6/5/x**2)+2)*ln(x**2)**8+16*ln(6/5/x**2)*ln(x**2)**7+40*x*ln(x**2)**6+240*x*ln(6/5/x**2)
*ln(x**2)**5+(150*x**2*ln(6/5/x**2)+300*x**2-100*x)*ln(x**2)**4+(1200*x**2-400*x)*ln(6/5/x**2)*ln(x**2)**3+((1
000*x**3-500*x**2)*ln(6/5/x**2)+1000*x**3-1000*x**2)*ln(x**2)**2+(2000*x**3-2000*x**2)*ln(6/5/x**2)*ln(x**2)+(
1875*x**4-2500*x**3+625*x**2)*ln(6/5/x**2)+1250*x**4-2500*x**3+1250*x**2)/x**2/ln(6/5/x**2)**2,x)

[Out]

x**2*(-500*log(6) + 500*log(5))/625 + x*(-450*log(5)**2*log(6) - 150*log(6)**3 - 500*log(5) + 150*log(5)**3 +
500*log(6) + 450*log(5)*log(6)**2)/625 - 4*(-log(6) + log(5))**2*(-4*log(5)*log(6) - 5 + 2*log(5)**2 + 2*log(6
)**2)*log(x)/125 + (-625*x**4 - 500*x**3*log(6)**2 - 500*x**3*log(5)**2 + 1250*x**3 + 1000*x**3*log(5)*log(6)
- 900*x**2*log(5)**2*log(6)**2 - 1000*x**2*log(5)*log(6) - 150*x**2*log(6)**4 - 150*x**2*log(5)**4 - 625*x**2
+ 500*x**2*log(5)**2 + 500*x**2*log(6)**2 + 600*x**2*log(5)**3*log(6) + 600*x**2*log(5)*log(6)**3 - 300*x*log(
5)**2*log(6)**4 - 300*x*log(5)**4*log(6)**2 - 200*x*log(5)*log(6)**3 - 200*x*log(5)**3*log(6) - 20*x*log(6)**6
- 20*x*log(5)**6 + 50*x*log(5)**4 + 50*x*log(6)**4 + 120*x*log(5)**5*log(6) + 300*x*log(5)**2*log(6)**2 + 120
*x*log(5)*log(6)**5 + 400*x*log(5)**3*log(6)**3 - 70*log(5)**4*log(6)**4 - 28*log(5)**2*log(6)**6 - 28*log(5)*
*6*log(6)**2 - log(6)**8 - log(5)**8 + 8*log(5)**7*log(6) + 8*log(5)*log(6)**7 + 56*log(5)**5*log(6)**3 + 56*l
og(5)**3*log(6)**5)/(625*x*log(x**2) - 625*x*log(6) + 625*x*log(5)) + (-20*x - log(6)**2 - log(5)**2 + 2*log(5
)*log(6))*log(x**2)**5/(625*x) + (-20*x*log(6) + 20*x*log(5) - 3*log(5)**2*log(6) - log(6)**3 + log(5)**3 + 3*
log(5)*log(6)**2)*log(x**2)**4/(625*x) + (-150*x**2 - 20*x*log(6)**2 - 20*x*log(5)**2 + 50*x + 40*x*log(5)*log
(6) - 6*log(5)**2*log(6)**2 - log(6)**4 - log(5)**4 + 4*log(5)**3*log(6) + 4*log(5)*log(6)**3)*log(x**2)**3/(6
25*x) + (-500*x**3 - 150*x**2*log(6)**2 - 150*x**2*log(5)**2 + 500*x**2 + 300*x**2*log(5)*log(6) - 15*log(5)**
2*log(6)**4 - 15*log(5)**4*log(6)**2 - log(6)**6 - log(5)**6 + 6*log(5)**5*log(6) + 6*log(5)*log(6)**5 + 20*lo
g(5)**3*log(6)**3)*log(x**2)/(625*x) + (-150*x**2*log(6) + 150*x**2*log(5) - 60*x*log(5)**2*log(6) - 20*x*log(
6)**3 - 50*x*log(5) + 20*x*log(5)**3 + 50*x*log(6) + 60*x*log(5)*log(6)**2 - 10*log(5)**2*log(6)**3 - 5*log(5)
**4*log(6) - log(6)**5 + log(5)**5 + 5*log(5)*log(6)**4 + 10*log(5)**3*log(6)**2)*log(x**2)**2/(625*x) - log(x
**2)**7/(625*x) + (-log(6) + log(5))*log(x**2)**6/(625*x) + (-35*log(5)**4*log(6)**3 - 21*log(5)**2*log(6)**5
- 7*log(5)**6*log(6) - log(6)**7 + log(5)**7 + 7*log(5)*log(6)**6 + 21*log(5)**5*log(6)**2 + 35*log(5)**3*log(
6)**4)/(625*x)

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