3.3.55 \(\int \frac {3750 x+300 x^2+6 x^3+(4000 x^2+300 x^3+6 x^4) \log (x)+((4000 x^2+310 x^3+6 x^4) \log (x)+(3750 x+300 x^2+6 x^3) \log (x) \log (\log (x))) \log (\frac {6400 x^2+480 x^3+9 x^4+(12000 x+930 x^2+18 x^3) \log (\log (x))+(5625+450 x+9 x^2) \log ^2(\log (x))}{5625+450 x+9 x^2})}{(2000 x+155 x^2+3 x^3) \log (x)+(1875+150 x+3 x^2) \log (x) \log (\log (x))} \, dx\)

Optimal. Leaf size=22 \[ x^2 \log \left (\left (x+\frac {5 x}{3 (25+x)}+\log (\log (x))\right )^2\right ) \]

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Rubi [A]  time = 8.62, antiderivative size = 32, normalized size of antiderivative = 1.45, number of steps used = 29, number of rules used = 5, integrand size = 175, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6688, 12, 6742, 30, 2555} \begin {gather*} x^2 \log \left (\frac {(x (3 x+80)+3 (x+25) \log (\log (x)))^2}{9 (x+25)^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3750*x + 300*x^2 + 6*x^3 + (4000*x^2 + 300*x^3 + 6*x^4)*Log[x] + ((4000*x^2 + 310*x^3 + 6*x^4)*Log[x] + (
3750*x + 300*x^2 + 6*x^3)*Log[x]*Log[Log[x]])*Log[(6400*x^2 + 480*x^3 + 9*x^4 + (12000*x + 930*x^2 + 18*x^3)*L
og[Log[x]] + (5625 + 450*x + 9*x^2)*Log[Log[x]]^2)/(5625 + 450*x + 9*x^2)])/((2000*x + 155*x^2 + 3*x^3)*Log[x]
+ (1875 + 150*x + 3*x^2)*Log[x]*Log[Log[x]]),x]

[Out]

x^2*Log[(x*(80 + 3*x) + 3*(25 + x)*Log[Log[x]])^2/(9*(25 + x)^2)]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 2555

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[w*Simplify
[D[u, x]/u], x], x] /; InverseFunctionFreeQ[w, x]] /; ProductQ[u]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (1875+150 x+3 x^2+x \left (2000+150 x+3 x^2\right ) \log (x)+(25+x) \log (x) (x (80+3 x)+3 (25+x) \log (\log (x))) \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )\right )}{(25+x) \log (x) (x (80+3 x)+3 (25+x) \log (\log (x)))} \, dx\\ &=2 \int \frac {x \left (1875+150 x+3 x^2+x \left (2000+150 x+3 x^2\right ) \log (x)+(25+x) \log (x) (x (80+3 x)+3 (25+x) \log (\log (x))) \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )\right )}{(25+x) \log (x) (x (80+3 x)+3 (25+x) \log (\log (x)))} \, dx\\ &=2 \int \left (\frac {x^2 \left (2000+150 x+3 x^2\right )}{(25+x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {1875 x}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {150 x^2}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {3 x^3}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+x \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )\right ) \, dx\\ &=2 \int \frac {x^2 \left (2000+150 x+3 x^2\right )}{(25+x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+2 \int x \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right ) \, dx+6 \int \frac {x^3}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+300 \int \frac {x^2}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+3750 \int \frac {x}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\\ &=x^2 \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )-2 \int \frac {x \left (3 (25+x)^2+x \left (2000+150 x+3 x^2\right ) \log (x)\right )}{(25+x) \log (x) (x (80+3 x)+3 (25+x) \log (\log (x)))} \, dx+2 \int \left (-\frac {3125}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))}+\frac {125 x}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))}+\frac {75 x^2}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))}+\frac {3 x^3}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))}+\frac {78125}{(25+x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}\right ) \, dx+6 \int \left (\frac {625}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}-\frac {25 x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {x^2}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}-\frac {15625}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}\right ) \, dx+300 \int \left (-\frac {25}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}+\frac {625}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}\right ) \, dx+3750 \int \left (\frac {1}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}-\frac {25}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}\right ) \, dx\\ &=x^2 \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )-2 \int \left (\frac {1875+150 x+3 x^2+2000 x \log (x)+150 x^2 \log (x)+3 x^3 \log (x)}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}-\frac {25 \left (1875+150 x+3 x^2+2000 x \log (x)+150 x^2 \log (x)+3 x^3 \log (x)\right )}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )}\right ) \, dx+6 \int \frac {x^3}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx+6 \int \frac {x^2}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+150 \int \frac {x^2}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx-150 \int \frac {x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+250 \int \frac {x}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx+300 \int \frac {x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+2 \left (3750 \int \frac {1}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\right )-6250 \int \frac {1}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx-7500 \int \frac {1}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx-2 \left (93750 \int \frac {1}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\right )+156250 \int \frac {1}{(25+x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+187500 \int \frac {1}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\\ &=x^2 \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right )-2 \int \frac {1875+150 x+3 x^2+2000 x \log (x)+150 x^2 \log (x)+3 x^3 \log (x)}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+6 \int \frac {x^3}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx+6 \int \frac {x^2}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+50 \int \frac {1875+150 x+3 x^2+2000 x \log (x)+150 x^2 \log (x)+3 x^3 \log (x)}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+150 \int \frac {x^2}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx-150 \int \frac {x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+250 \int \frac {x}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx+300 \int \frac {x}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+2 \left (3750 \int \frac {1}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\right )-6250 \int \frac {1}{80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))} \, dx-7500 \int \frac {1}{\log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx-2 \left (93750 \int \frac {1}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\right )+156250 \int \frac {1}{(25+x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx+187500 \int \frac {1}{(25+x) \log (x) \left (80 x+3 x^2+75 \log (\log (x))+3 x \log (\log (x))\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 32, normalized size = 1.45 \begin {gather*} x^2 \log \left (\frac {(x (80+3 x)+3 (25+x) \log (\log (x)))^2}{9 (25+x)^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3750*x + 300*x^2 + 6*x^3 + (4000*x^2 + 300*x^3 + 6*x^4)*Log[x] + ((4000*x^2 + 310*x^3 + 6*x^4)*Log[
x] + (3750*x + 300*x^2 + 6*x^3)*Log[x]*Log[Log[x]])*Log[(6400*x^2 + 480*x^3 + 9*x^4 + (12000*x + 930*x^2 + 18*
x^3)*Log[Log[x]] + (5625 + 450*x + 9*x^2)*Log[Log[x]]^2)/(5625 + 450*x + 9*x^2)])/((2000*x + 155*x^2 + 3*x^3)*
Log[x] + (1875 + 150*x + 3*x^2)*Log[x]*Log[Log[x]]),x]

[Out]

x^2*Log[(x*(80 + 3*x) + 3*(25 + x)*Log[Log[x]])^2/(9*(25 + x)^2)]

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fricas [B]  time = 0.99, size = 67, normalized size = 3.05 \begin {gather*} x^{2} \log \left (\frac {9 \, x^{4} + 480 \, x^{3} + 9 \, {\left (x^{2} + 50 \, x + 625\right )} \log \left (\log \relax (x)\right )^{2} + 6400 \, x^{2} + 6 \, {\left (3 \, x^{3} + 155 \, x^{2} + 2000 \, x\right )} \log \left (\log \relax (x)\right )}{9 \, {\left (x^{2} + 50 \, x + 625\right )}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000*x^2)*log(x))*log(((9*x^2+450*x+5625)
*log(log(x))^2+(18*x^3+930*x^2+12000*x)*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3
+4000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x))+(3*x^3+155*x^2+2000*x)*log(x)),
x, algorithm="fricas")

[Out]

x^2*log(1/9*(9*x^4 + 480*x^3 + 9*(x^2 + 50*x + 625)*log(log(x))^2 + 6400*x^2 + 6*(3*x^3 + 155*x^2 + 2000*x)*lo
g(log(x)))/(x^2 + 50*x + 625))

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giac [B]  time = 102.74, size = 85, normalized size = 3.86 \begin {gather*} x^{2} \log \left (9 \, x^{4} + 18 \, x^{3} \log \left (\log \relax (x)\right ) + 9 \, x^{2} \log \left (\log \relax (x)\right )^{2} + 480 \, x^{3} + 930 \, x^{2} \log \left (\log \relax (x)\right ) + 450 \, x \log \left (\log \relax (x)\right )^{2} + 6400 \, x^{2} + 12000 \, x \log \left (\log \relax (x)\right ) + 5625 \, \log \left (\log \relax (x)\right )^{2}\right ) - x^{2} \log \left (9 \, x^{2} + 450 \, x + 5625\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000*x^2)*log(x))*log(((9*x^2+450*x+5625)
*log(log(x))^2+(18*x^3+930*x^2+12000*x)*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3
+4000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x))+(3*x^3+155*x^2+2000*x)*log(x)),
x, algorithm="giac")

[Out]

x^2*log(9*x^4 + 18*x^3*log(log(x)) + 9*x^2*log(log(x))^2 + 480*x^3 + 930*x^2*log(log(x)) + 450*x*log(log(x))^2
+ 6400*x^2 + 12000*x*log(log(x)) + 5625*log(log(x))^2) - x^2*log(9*x^2 + 450*x + 5625)

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maple [C]  time = 0.47, size = 438, normalized size = 19.91

method	result	size
risch	\(2 x^{2} \ln \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )-2 x^{2} \ln \left (x +25\right )-\frac {i \pi \,x^{2} \mathrm {csgn}\left (\frac {i}{\left (x +25\right )^{2}}\right ) \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )}{2}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (\frac {i}{\left (x +25\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )^{2}}{2}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +25\right )\right )^{2} \mathrm {csgn}\left (i \left (x +25\right )^{2}\right )}{2}-i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +25\right )\right ) \mathrm {csgn}\left (i \left (x +25\right )^{2}\right )^{2}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i \left (x +25\right )^{2}\right )^{3}}{2}-\frac {i \pi \,x^{2} \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )\right )^{2} \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}\right )}{2}+i \pi \,x^{2} \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )\right ) \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}\right )^{2}-\frac {i \pi \,x^{2} \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}\right )^{3}}{2}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )^{2}}{2}-\frac {i \pi \,x^{2} \mathrm {csgn}\left (\frac {i \left (x^{2}+\left (\ln \left (\ln \relax (x )\right )+\frac {80}{3}\right ) x +25 \ln \left (\ln \relax (x )\right )\right )^{2}}{\left (x +25\right )^{2}}\right )^{3}}{2}\)	\(438\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((6*x^3+300*x^2+3750*x)*ln(x)*ln(ln(x))+(6*x^4+310*x^3+4000*x^2)*ln(x))*ln(((9*x^2+450*x+5625)*ln(ln(x))^
2+(18*x^3+930*x^2+12000*x)*ln(ln(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3+4000*x^2)*ln(x
)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*ln(x)*ln(ln(x))+(3*x^3+155*x^2+2000*x)*ln(x)),x,method=_RETURNVERB
OSE)

[Out]

2*x^2*ln(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))-2*x^2*ln(x+25)-1/2*I*Pi*x^2*csgn(I/(x+25)^2)*csgn(I*(x^2+(ln(ln(
x))+80/3)*x+25*ln(ln(x)))^2)*csgn(I/(x+25)^2*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)+1/2*I*Pi*x^2*csgn(I/(x+2
5)^2)*csgn(I/(x+25)^2*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)^2+1/2*I*Pi*x^2*csgn(I*(x+25))^2*csgn(I*(x+25)^2
)-I*Pi*x^2*csgn(I*(x+25))*csgn(I*(x+25)^2)^2+1/2*I*Pi*x^2*csgn(I*(x+25)^2)^3-1/2*I*Pi*x^2*csgn(I*(x^2+(ln(ln(x
))+80/3)*x+25*ln(ln(x))))^2*csgn(I*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)+I*Pi*x^2*csgn(I*(x^2+(ln(ln(x))+80
/3)*x+25*ln(ln(x))))*csgn(I*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)^2-1/2*I*Pi*x^2*csgn(I*(x^2+(ln(ln(x))+80/
3)*x+25*ln(ln(x)))^2)^3+1/2*I*Pi*x^2*csgn(I*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)*csgn(I/(x+25)^2*(x^2+(ln(
ln(x))+80/3)*x+25*ln(ln(x)))^2)^2-1/2*I*Pi*x^2*csgn(I/(x+25)^2*(x^2+(ln(ln(x))+80/3)*x+25*ln(ln(x)))^2)^3

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maxima [A]  time = 0.53, size = 40, normalized size = 1.82 \begin {gather*} -2 \, x^{2} \log \relax (3) + 2 \, x^{2} \log \left (3 \, x^{2} + 3 \, {\left (x + 25\right )} \log \left (\log \relax (x)\right ) + 80 \, x\right ) - 2 \, x^{2} \log \left (x + 25\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x^3+300*x^2+3750*x)*log(x)*log(log(x))+(6*x^4+310*x^3+4000*x^2)*log(x))*log(((9*x^2+450*x+5625)
*log(log(x))^2+(18*x^3+930*x^2+12000*x)*log(log(x))+9*x^4+480*x^3+6400*x^2)/(9*x^2+450*x+5625))+(6*x^4+300*x^3
+4000*x^2)*log(x)+6*x^3+300*x^2+3750*x)/((3*x^2+150*x+1875)*log(x)*log(log(x))+(3*x^3+155*x^2+2000*x)*log(x)),
x, algorithm="maxima")

[Out]

-2*x^2*log(3) + 2*x^2*log(3*x^2 + 3*(x + 25)*log(log(x)) + 80*x) - 2*x^2*log(x + 25)

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mupad [B]  time = 1.30, size = 68, normalized size = 3.09 \begin {gather*} x^2\,\ln \left (\frac {\ln \left (\ln \relax (x)\right )\,\left (18\,x^3+930\,x^2+12000\,x\right )+{\ln \left (\ln \relax (x)\right )}^2\,\left (9\,x^2+450\,x+5625\right )+6400\,x^2+480\,x^3+9\,x^4}{9\,x^2+450\,x+5625}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3750*x + log(x)*(4000*x^2 + 300*x^3 + 6*x^4) + log((log(log(x))*(12000*x + 930*x^2 + 18*x^3) + log(log(x)
)^2*(450*x + 9*x^2 + 5625) + 6400*x^2 + 480*x^3 + 9*x^4)/(450*x + 9*x^2 + 5625))*(log(x)*(4000*x^2 + 310*x^3 +
6*x^4) + log(log(x))*log(x)*(3750*x + 300*x^2 + 6*x^3)) + 300*x^2 + 6*x^3)/(log(x)*(2000*x + 155*x^2 + 3*x^3)
+ log(log(x))*log(x)*(150*x + 3*x^2 + 1875)),x)

[Out]

x^2*log((log(log(x))*(12000*x + 930*x^2 + 18*x^3) + log(log(x))^2*(450*x + 9*x^2 + 5625) + 6400*x^2 + 480*x^3
+ 9*x^4)/(450*x + 9*x^2 + 5625))

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sympy [B]  time = 4.09, size = 92, normalized size = 4.18 \begin {gather*} \left (x^{2} - \frac {625}{6}\right ) \log {\left (\frac {9 x^{4} + 480 x^{3} + 6400 x^{2} + \left (9 x^{2} + 450 x + 5625\right ) \log {\left (\log {\relax (x )} \right )}^{2} + \left (18 x^{3} + 930 x^{2} + 12000 x\right ) \log {\left (\log {\relax (x )} \right )}}{9 x^{2} + 450 x + 5625} \right )} + \frac {625 \log {\left (\log {\left (\log {\relax (x )} \right )} + \frac {3 x^{2} + 80 x}{3 x + 75} \right )}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((6*x**3+300*x**2+3750*x)*ln(x)*ln(ln(x))+(6*x**4+310*x**3+4000*x**2)*ln(x))*ln(((9*x**2+450*x+5625
)*ln(ln(x))**2+(18*x**3+930*x**2+12000*x)*ln(ln(x))+9*x**4+480*x**3+6400*x**2)/(9*x**2+450*x+5625))+(6*x**4+30
0*x**3+4000*x**2)*ln(x)+6*x**3+300*x**2+3750*x)/((3*x**2+150*x+1875)*ln(x)*ln(ln(x))+(3*x**3+155*x**2+2000*x)*
ln(x)),x)

[Out]

(x**2 - 625/6)*log((9*x**4 + 480*x**3 + 6400*x**2 + (9*x**2 + 450*x + 5625)*log(log(x))**2 + (18*x**3 + 930*x*
*2 + 12000*x)*log(log(x)))/(9*x**2 + 450*x + 5625)) + 625*log(log(log(x)) + (3*x**2 + 80*x)/(3*x + 75))/3

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