3.24.3 \(\int \frac {-960 x+1152 x \log (150 x \log (5))+(592 x-960 x \log (150 x \log (5))) \log (\log ^2(150 x \log (5)))+(-120 x+296 x \log (150 x \log (5))) \log ^2(\log ^2(150 x \log (5)))+(8 x-40 x \log (150 x \log (5))) \log ^3(\log ^2(150 x \log (5)))+2 x \log (150 x \log (5)) \log ^4(\log ^2(150 x \log (5)))}{\log (150 x \log (5))} \, dx\)

Optimal. Leaf size=23 \[ \left (x+x \left (-2+\left (5-\log \left (\log ^2(150 x \log (5))\right )\right )^2\right )\right )^2 \]

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Rubi [A]  time = 0.15, antiderivative size = 30, normalized size of antiderivative = 1.30, number of steps used = 3, number of rules used = 3, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6688, 12, 6687} \begin {gather*} x^2 \left (\log ^2\left (\log ^2(150 x \log (5))\right )-10 \log \left (\log ^2(150 x \log (5))\right )+24\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-960*x + 1152*x*Log[150*x*Log[5]] + (592*x - 960*x*Log[150*x*Log[5]])*Log[Log[150*x*Log[5]]^2] + (-120*x
+ 296*x*Log[150*x*Log[5]])*Log[Log[150*x*Log[5]]^2]^2 + (8*x - 40*x*Log[150*x*Log[5]])*Log[Log[150*x*Log[5]]^2
]^3 + 2*x*Log[150*x*Log[5]]*Log[Log[150*x*Log[5]]^2]^4)/Log[150*x*Log[5]],x]

[Out]

x^2*(24 - 10*Log[Log[150*x*Log[5]]^2] + Log[Log[150*x*Log[5]]^2]^2)^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 6687

Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y*z, u*z^(n - m), x]}, Simp[(q*y^(m +
1)*z^(m + 1))/(m + 1), x] /;  !FalseQ[q]] /; FreeQ[{m, n}, x] && NeQ[m, -1]

Rule 6688

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (24-10 \log \left (\log ^2(150 x \log (5))\right )+\log ^2\left (\log ^2(150 x \log (5))\right )\right ) \left (4 \left (-5+\log \left (\log ^2(150 x \log (5))\right )\right )+\log (150 x \log (5)) \left (24-10 \log \left (\log ^2(150 x \log (5))\right )+\log ^2\left (\log ^2(150 x \log (5))\right )\right )\right )}{\log (150 x \log (5))} \, dx\\ &=2 \int \frac {x \left (24-10 \log \left (\log ^2(150 x \log (5))\right )+\log ^2\left (\log ^2(150 x \log (5))\right )\right ) \left (4 \left (-5+\log \left (\log ^2(150 x \log (5))\right )\right )+\log (150 x \log (5)) \left (24-10 \log \left (\log ^2(150 x \log (5))\right )+\log ^2\left (\log ^2(150 x \log (5))\right )\right )\right )}{\log (150 x \log (5))} \, dx\\ &=x^2 \left (24-10 \log \left (\log ^2(150 x \log (5))\right )+\log ^2\left (\log ^2(150 x \log (5))\right )\right )^2\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.16, size = 67, normalized size = 2.91 \begin {gather*} 576 x^2-480 x^2 \log \left (\log ^2(150 x \log (5))\right )+148 x^2 \log ^2\left (\log ^2(150 x \log (5))\right )-20 x^2 \log ^3\left (\log ^2(150 x \log (5))\right )+x^2 \log ^4\left (\log ^2(150 x \log (5))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-960*x + 1152*x*Log[150*x*Log[5]] + (592*x - 960*x*Log[150*x*Log[5]])*Log[Log[150*x*Log[5]]^2] + (-
120*x + 296*x*Log[150*x*Log[5]])*Log[Log[150*x*Log[5]]^2]^2 + (8*x - 40*x*Log[150*x*Log[5]])*Log[Log[150*x*Log
[5]]^2]^3 + 2*x*Log[150*x*Log[5]]*Log[Log[150*x*Log[5]]^2]^4)/Log[150*x*Log[5]],x]

[Out]

576*x^2 - 480*x^2*Log[Log[150*x*Log[5]]^2] + 148*x^2*Log[Log[150*x*Log[5]]^2]^2 - 20*x^2*Log[Log[150*x*Log[5]]
^2]^3 + x^2*Log[Log[150*x*Log[5]]^2]^4

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fricas [B]  time = 0.71, size = 67, normalized size = 2.91 \begin {gather*} x^{2} \log \left (\log \left (150 \, x \log \relax (5)\right )^{2}\right )^{4} - 20 \, x^{2} \log \left (\log \left (150 \, x \log \relax (5)\right )^{2}\right )^{3} + 148 \, x^{2} \log \left (\log \left (150 \, x \log \relax (5)\right )^{2}\right )^{2} - 480 \, x^{2} \log \left (\log \left (150 \, x \log \relax (5)\right )^{2}\right ) + 576 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(150*x*log(5))*log(log(150*x*log(5))^2)^4+(-40*x*log(150*x*log(5))+8*x)*log(log(150*x*log(5)
)^2)^3+(296*x*log(150*x*log(5))-120*x)*log(log(150*x*log(5))^2)^2+(-960*x*log(150*x*log(5))+592*x)*log(log(150
*x*log(5))^2)+1152*x*log(150*x*log(5))-960*x)/log(150*x*log(5)),x, algorithm="fricas")

[Out]

x^2*log(log(150*x*log(5))^2)^4 - 20*x^2*log(log(150*x*log(5))^2)^3 + 148*x^2*log(log(150*x*log(5))^2)^2 - 480*
x^2*log(log(150*x*log(5))^2) + 576*x^2

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giac [B]  time = 2.17, size = 64, normalized size = 2.78 \begin {gather*} 16 \, x^{2} \log \left ({\left | \log \left (150 \, x \log \relax (5)\right ) \right |}\right )^{4} - 160 \, x^{2} \log \left ({\left | \log \left (150 \, x \log \relax (5)\right ) \right |}\right )^{3} + 592 \, x^{2} \log \left ({\left | \log \left (150 \, x \log \relax (5)\right ) \right |}\right )^{2} - 960 \, x^{2} \log \left ({\left | \log \left (150 \, x \log \relax (5)\right ) \right |}\right ) + 576 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(150*x*log(5))*log(log(150*x*log(5))^2)^4+(-40*x*log(150*x*log(5))+8*x)*log(log(150*x*log(5)
)^2)^3+(296*x*log(150*x*log(5))-120*x)*log(log(150*x*log(5))^2)^2+(-960*x*log(150*x*log(5))+592*x)*log(log(150
*x*log(5))^2)+1152*x*log(150*x*log(5))-960*x)/log(150*x*log(5)),x, algorithm="giac")

[Out]

16*x^2*log(abs(log(150*x*log(5))))^4 - 160*x^2*log(abs(log(150*x*log(5))))^3 + 592*x^2*log(abs(log(150*x*log(5
))))^2 - 960*x^2*log(abs(log(150*x*log(5)))) + 576*x^2

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maple [C]  time = 0.57, size = 1463, normalized size = 63.61

method	result	size
risch	\(16 x^{2} \ln \left (\ln \left (150 x \ln \relax (5)\right )\right )^{4}-16 i x^{2} \left (\pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )-2 \pi \,\mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}+\pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}-10 i\right ) \ln \left (\ln \left (150 x \ln \relax (5)\right )\right )^{3}-2 x^{2} \left (3 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}-12 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}+18 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}-12 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}+3 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}-60 i \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )+120 i \pi \,\mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}-60 i \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}-296\right ) \ln \left (\ln \left (150 x \ln \relax (5)\right )\right )^{2}+i x^{2} \left (\pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{6} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}-6 \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{5} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}+15 \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}-20 \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}+15 \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{7}-6 \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{8}+\pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{9}-180 i \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}+120 i \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}-30 i \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}+120 i \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}-30 i \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}-296 \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )+592 \pi \,\mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}-296 \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}+960 i\right ) \ln \left (\ln \left (150 x \ln \relax (5)\right )\right )+\frac {x^{2} \left (9216-592 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}+2368 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}-3552 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}+2368 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}+3840 i \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}+\pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{8} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}-8 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{7} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}+28 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{6} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}-56 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{5} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{7}+70 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{8}-56 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{9}+28 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{10}-8 \pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{11}-40 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{9}-600 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{5}+3840 i \pi \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )-7680 i \pi \,\mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{2}+800 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}-600 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{7}+240 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right ) \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{8}-40 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{6} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{3}+240 i \pi ^{3} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )\right )^{5} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{4}+\pi ^{4} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{12}-592 \pi ^{2} \mathrm {csgn}\left (i \ln \left (150 x \ln \relax (5)\right )^{2}\right )^{6}\right )}{16}\)	\(1463\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x*ln(150*x*ln(5))*ln(ln(150*x*ln(5))^2)^4+(-40*x*ln(150*x*ln(5))+8*x)*ln(ln(150*x*ln(5))^2)^3+(296*x*ln
(150*x*ln(5))-120*x)*ln(ln(150*x*ln(5))^2)^2+(-960*x*ln(150*x*ln(5))+592*x)*ln(ln(150*x*ln(5))^2)+1152*x*ln(15
0*x*ln(5))-960*x)/ln(150*x*ln(5)),x,method=_RETURNVERBOSE)

[Out]

16*x^2*ln(ln(150*x*ln(5)))^4-16*I*x^2*(Pi*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2)-2*Pi*csgn(I*ln(1
50*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^2+Pi*csgn(I*ln(150*x*ln(5))^2)^3-10*I)*ln(ln(150*x*ln(5)))^3-2*x^2*(3*P
i^2*csgn(I*ln(150*x*ln(5)))^4*csgn(I*ln(150*x*ln(5))^2)^2-12*Pi^2*csgn(I*ln(150*x*ln(5)))^3*csgn(I*ln(150*x*ln
(5))^2)^3+18*Pi^2*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2)^4-12*Pi^2*csgn(I*ln(150*x*ln(5)))*csgn(I
*ln(150*x*ln(5))^2)^5+3*Pi^2*csgn(I*ln(150*x*ln(5))^2)^6-60*I*Pi*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(
5))^2)+120*I*Pi*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^2-60*I*Pi*csgn(I*ln(150*x*ln(5))^2)^3-296)*l
n(ln(150*x*ln(5)))^2+I*x^2*(Pi^3*csgn(I*ln(150*x*ln(5)))^6*csgn(I*ln(150*x*ln(5))^2)^3-6*Pi^3*csgn(I*ln(150*x*
ln(5)))^5*csgn(I*ln(150*x*ln(5))^2)^4+15*Pi^3*csgn(I*ln(150*x*ln(5)))^4*csgn(I*ln(150*x*ln(5))^2)^5-20*Pi^3*cs
gn(I*ln(150*x*ln(5)))^3*csgn(I*ln(150*x*ln(5))^2)^6+15*Pi^3*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2
)^7-6*Pi^3*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^8+Pi^3*csgn(I*ln(150*x*ln(5))^2)^9-180*I*Pi^2*csg
n(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2)^4+120*I*Pi^2*csgn(I*ln(150*x*ln(5)))^3*csgn(I*ln(150*x*ln(5))
^2)^3-30*I*Pi^2*csgn(I*ln(150*x*ln(5)))^4*csgn(I*ln(150*x*ln(5))^2)^2+120*I*Pi^2*csgn(I*ln(150*x*ln(5)))*csgn(
I*ln(150*x*ln(5))^2)^5-30*I*Pi^2*csgn(I*ln(150*x*ln(5))^2)^6-296*Pi*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*
ln(5))^2)+592*Pi*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^2-296*Pi*csgn(I*ln(150*x*ln(5))^2)^3+960*I)
*ln(ln(150*x*ln(5)))+1/16*x^2*(9216+Pi^4*csgn(I*ln(150*x*ln(5)))^8*csgn(I*ln(150*x*ln(5))^2)^4-8*Pi^4*csgn(I*l
n(150*x*ln(5)))^7*csgn(I*ln(150*x*ln(5))^2)^5+28*Pi^4*csgn(I*ln(150*x*ln(5)))^6*csgn(I*ln(150*x*ln(5))^2)^6-56
*Pi^4*csgn(I*ln(150*x*ln(5)))^5*csgn(I*ln(150*x*ln(5))^2)^7+70*Pi^4*csgn(I*ln(150*x*ln(5)))^4*csgn(I*ln(150*x*
ln(5))^2)^8-56*Pi^4*csgn(I*ln(150*x*ln(5)))^3*csgn(I*ln(150*x*ln(5))^2)^9+28*Pi^4*csgn(I*ln(150*x*ln(5)))^2*cs
gn(I*ln(150*x*ln(5))^2)^10-8*Pi^4*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^11+3840*I*Pi*csgn(I*ln(150
*x*ln(5))^2)^3-40*I*Pi^3*csgn(I*ln(150*x*ln(5))^2)^9+3840*I*Pi*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5)
)^2)-7680*I*Pi*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^2+800*I*Pi^3*csgn(I*ln(150*x*ln(5)))^3*csgn(I
*ln(150*x*ln(5))^2)^6-600*I*Pi^3*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2)^7+240*I*Pi^3*csgn(I*ln(15
0*x*ln(5)))*csgn(I*ln(150*x*ln(5))^2)^8-40*I*Pi^3*csgn(I*ln(150*x*ln(5)))^6*csgn(I*ln(150*x*ln(5))^2)^3+240*I*
Pi^3*csgn(I*ln(150*x*ln(5)))^5*csgn(I*ln(150*x*ln(5))^2)^4-600*I*Pi^3*csgn(I*ln(150*x*ln(5)))^4*csgn(I*ln(150*
x*ln(5))^2)^5-592*Pi^2*csgn(I*ln(150*x*ln(5))^2)^6+Pi^4*csgn(I*ln(150*x*ln(5))^2)^12-592*Pi^2*csgn(I*ln(150*x*
ln(5)))^4*csgn(I*ln(150*x*ln(5))^2)^2+2368*Pi^2*csgn(I*ln(150*x*ln(5)))^3*csgn(I*ln(150*x*ln(5))^2)^3-3552*Pi^
2*csgn(I*ln(150*x*ln(5)))^2*csgn(I*ln(150*x*ln(5))^2)^4+2368*Pi^2*csgn(I*ln(150*x*ln(5)))*csgn(I*ln(150*x*ln(5
))^2)^5)

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maxima [B]  time = 1.07, size = 86, normalized size = 3.74 \begin {gather*} 16 \, x^{2} \log \left (2 \, \log \relax (5) + \log \relax (3) + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (5)\right )\right )^{4} - 160 \, x^{2} \log \left (2 \, \log \relax (5) + \log \relax (3) + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (5)\right )\right )^{3} + 592 \, x^{2} \log \left (2 \, \log \relax (5) + \log \relax (3) + \log \relax (2) + \log \relax (x) + \log \left (\log \relax (5)\right )\right )^{2} - 480 \, x^{2} \log \left (\log \left (150 \, x \log \relax (5)\right )^{2}\right ) + 576 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(150*x*log(5))*log(log(150*x*log(5))^2)^4+(-40*x*log(150*x*log(5))+8*x)*log(log(150*x*log(5)
)^2)^3+(296*x*log(150*x*log(5))-120*x)*log(log(150*x*log(5))^2)^2+(-960*x*log(150*x*log(5))+592*x)*log(log(150
*x*log(5))^2)+1152*x*log(150*x*log(5))-960*x)/log(150*x*log(5)),x, algorithm="maxima")

[Out]

16*x^2*log(2*log(5) + log(3) + log(2) + log(x) + log(log(5)))^4 - 160*x^2*log(2*log(5) + log(3) + log(2) + log
(x) + log(log(5)))^3 + 592*x^2*log(2*log(5) + log(3) + log(2) + log(x) + log(log(5)))^2 - 480*x^2*log(log(150*
x*log(5))^2) + 576*x^2

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mupad [B]  time = 1.42, size = 67, normalized size = 2.91 \begin {gather*} x^2\,{\ln \left ({\ln \left (150\,x\,\ln \relax (5)\right )}^2\right )}^4-20\,x^2\,{\ln \left ({\ln \left (150\,x\,\ln \relax (5)\right )}^2\right )}^3+148\,x^2\,{\ln \left ({\ln \left (150\,x\,\ln \relax (5)\right )}^2\right )}^2-480\,x^2\,\ln \left ({\ln \left (150\,x\,\ln \relax (5)\right )}^2\right )+576\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1152*x*log(150*x*log(5)) - 960*x + log(log(150*x*log(5))^2)*(592*x - 960*x*log(150*x*log(5))) + log(log(1
50*x*log(5))^2)^3*(8*x - 40*x*log(150*x*log(5))) - log(log(150*x*log(5))^2)^2*(120*x - 296*x*log(150*x*log(5))
) + 2*x*log(log(150*x*log(5))^2)^4*log(150*x*log(5)))/log(150*x*log(5)),x)

[Out]

148*x^2*log(log(150*x*log(5))^2)^2 - 20*x^2*log(log(150*x*log(5))^2)^3 + x^2*log(log(150*x*log(5))^2)^4 - 480*
x^2*log(log(150*x*log(5))^2) + 576*x^2

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sympy [B]  time = 0.68, size = 75, normalized size = 3.26 \begin {gather*} x^{2} \log {\left (\log {\left (150 x \log {\relax (5 )} \right )}^{2} \right )}^{4} - 20 x^{2} \log {\left (\log {\left (150 x \log {\relax (5 )} \right )}^{2} \right )}^{3} + 148 x^{2} \log {\left (\log {\left (150 x \log {\relax (5 )} \right )}^{2} \right )}^{2} - 480 x^{2} \log {\left (\log {\left (150 x \log {\relax (5 )} \right )}^{2} \right )} + 576 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*ln(150*x*ln(5))*ln(ln(150*x*ln(5))**2)**4+(-40*x*ln(150*x*ln(5))+8*x)*ln(ln(150*x*ln(5))**2)**3
+(296*x*ln(150*x*ln(5))-120*x)*ln(ln(150*x*ln(5))**2)**2+(-960*x*ln(150*x*ln(5))+592*x)*ln(ln(150*x*ln(5))**2)
+1152*x*ln(150*x*ln(5))-960*x)/ln(150*x*ln(5)),x)

[Out]

x**2*log(log(150*x*log(5))**2)**4 - 20*x**2*log(log(150*x*log(5))**2)**3 + 148*x**2*log(log(150*x*log(5))**2)*
*2 - 480*x**2*log(log(150*x*log(5))**2) + 576*x**2

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