3.35.12 \(\int \frac {-200 x^3-80 x^3 \log (2)-8 x^3 \log ^2(2)+(24000 x^2+3100 x^3+(9600 x^2+1240 x^3) \log (2)+(960 x^2+124 x^3) \log ^2(2)) \log (x^2)+(-960000 x-252000 x^2-17000 x^3+(-384000 x-100800 x^2-6800 x^3) \log (2)+(-38400 x-10080 x^2-680 x^3) \log ^2(2)) \log ^2(x^2)+(12800000+5280000 x+780000 x^2+40000 x^3+(5120000+2112000 x+312000 x^2+16000 x^3) \log (2)+(512000+211200 x+31200 x^2+1600 x^3) \log ^2(2)) \log ^3(x^2)+(-6400000-4800000 x-900000 x^2-50000 x^3+(-2560000-1920000 x-360000 x^2-20000 x^3) \log (2)+(-256000-192000 x-36000 x^2-2000 x^3) \log ^2(2)) \log ^4(x^2)+(31999975+12000000 x+1500000 x^2+62500 x^3+(12800000+4800000 x+600000 x^2+25000 x^3) \log (2)+(1280000+480000 x+60000 x^2+2500 x^3) \log ^2(2)) \log ^5(x^2)}{25 \log ^5(x^2)} \, dx\) [3412]

Optimal. Leaf size=28 \[ -x+25 (5+\log (2))^2 \left (8+x-\frac {x}{5 \log \left (x^2\right )}\right )^4 \]

[Out]

25*(ln(2)+5)^2*(8+x-1/5*x/ln(x^2))^4-x

________________________________________________________________________________________

Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(222\) vs. \(2(28)=56\).
time = 1.04, antiderivative size = 222, normalized size of antiderivative = 7.93, number of steps used = 62, number of rules used = 12, integrand size = 315, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6, 12, 6820, 2343, 2347, 2209, 2395, 2403, 2344, 2335, 2334, 2337} \begin {gather*} 25 x^4 (5+\log (2))^2+800 x^3 (5+\log (2))^2+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}+9600 x^2 (5+\log (2))^2-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}+x \left (1279999+51200 \log ^2(2)+512000 \log (2)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-200*x^3 - 80*x^3*Log[2] - 8*x^3*Log[2]^2 + (24000*x^2 + 3100*x^3 + (9600*x^2 + 1240*x^3)*Log[2] + (960*x
^2 + 124*x^3)*Log[2]^2)*Log[x^2] + (-960000*x - 252000*x^2 - 17000*x^3 + (-384000*x - 100800*x^2 - 6800*x^3)*L
og[2] + (-38400*x - 10080*x^2 - 680*x^3)*Log[2]^2)*Log[x^2]^2 + (12800000 + 5280000*x + 780000*x^2 + 40000*x^3
+ (5120000 + 2112000*x + 312000*x^2 + 16000*x^3)*Log[2] + (512000 + 211200*x + 31200*x^2 + 1600*x^3)*Log[2]^2
)*Log[x^2]^3 + (-6400000 - 4800000*x - 900000*x^2 - 50000*x^3 + (-2560000 - 1920000*x - 360000*x^2 - 20000*x^3
)*Log[2] + (-256000 - 192000*x - 36000*x^2 - 2000*x^3)*Log[2]^2)*Log[x^2]^4 + (31999975 + 12000000*x + 1500000
*x^2 + 62500*x^3 + (12800000 + 4800000*x + 600000*x^2 + 25000*x^3)*Log[2] + (1280000 + 480000*x + 60000*x^2 +
2500*x^3)*Log[2]^2)*Log[x^2]^5)/(25*Log[x^2]^5),x]

[Out]

9600*x^2*(5 + Log[2])^2 + 800*x^3*(5 + Log[2])^2 + 25*x^4*(5 + Log[2])^2 + x*(1279999 + 512000*Log[2] + 51200*
Log[2]^2) + (x^4*(5 + Log[2])^2)/(25*Log[x^2]^4) - (32*x^3*(5 + Log[2])^2)/(5*Log[x^2]^3) - (4*x^4*(5 + Log[2]
)^2)/(5*Log[x^2]^3) + (384*x^2*(5 + Log[2])^2)/Log[x^2]^2 + (96*x^3*(5 + Log[2])^2)/Log[x^2]^2 + (6*x^4*(5 + L
og[2])^2)/Log[x^2]^2 - (10240*x*(5 + Log[2])^2)/Log[x^2] - (3840*x^2*(5 + Log[2])^2)/Log[x^2] - (480*x^3*(5 +
Log[2])^2)/Log[x^2] - (20*x^4*(5 + Log[2])^2)/Log[x^2]

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

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

Rule 2209

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - c*(f/d)))/d)*ExpInteg
ralEi[f*g*(c + d*x)*(Log[F]/d)], x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !TrueQ[$UseGamma]

Rule 2334

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_), x_Symbol] :> Simp[x*((a + b*Log[c*x^n])^(p + 1)/(b*n*(p + 1)))
, x] - Dist[1/(b*n*(p + 1)), Int[(a + b*Log[c*x^n])^(p + 1), x], x] /; FreeQ[{a, b, c, n}, x] && LtQ[p, -1] &&
IntegerQ[2*p]

Rule 2335

Int[Log[(c_.)*(x_)]^(-1), x_Symbol] :> Simp[LogIntegral[c*x]/c, x] /; FreeQ[c, x]

Rule 2337

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_), x_Symbol] :> Dist[x/(n*(c*x^n)^(1/n)), Subst[Int[E^(x/n)*(a +
b*x)^p, x], x, Log[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]

Rule 2343

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log
[c*x^n])^(p + 1)/(b*d*n*(p + 1))), x] - Dist[(m + 1)/(b*n*(p + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p + 1), x]
, x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1] && LtQ[p, -1]

Rule 2344

Int[(x_)^(m_.)/Log[(c_.)*(x_)^(n_)], x_Symbol] :> Dist[1/n, Subst[Int[1/Log[c*x], x], x, x^n], x] /; FreeQ[{c,
m, n}, x] && EqQ[m, n - 1]

Rule 2347

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_)*((d_.)*(x_))^(m_.), x_Symbol] :> Dist[(d*x)^(m + 1)/(d*n*(c*x^n
)^((m + 1)/n)), Subst[Int[E^(((m + 1)/n)*x)*(a + b*x)^p, x], x, Log[c*x^n]], x] /; FreeQ[{a, b, c, d, m, n, p}
, x]

Rule 2395

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol]
:> With[{u = ExpandIntegrand[(a + b*Log[c*x^n])^p, (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[
{a, b, c, d, e, f, m, n, p, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[m] && IntegerQ[r
]))

Rule 2403

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rule 6820

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 {x^3 (-200-80 \log (2))-8 x^3 \log ^2(2)+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx\\ &=\int \frac {x^3 \left (-200-80 \log (2)-8 \log ^2(2)\right )+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{25 \log ^5\left (x^2\right )} \, dx\\ &=\frac {1}{25} \int \frac {x^3 \left (-200-80 \log (2)-8 \log ^2(2)\right )+\left (24000 x^2+3100 x^3+\left (9600 x^2+1240 x^3\right ) \log (2)+\left (960 x^2+124 x^3\right ) \log ^2(2)\right ) \log \left (x^2\right )+\left (-960000 x-252000 x^2-17000 x^3+\left (-384000 x-100800 x^2-6800 x^3\right ) \log (2)+\left (-38400 x-10080 x^2-680 x^3\right ) \log ^2(2)\right ) \log ^2\left (x^2\right )+\left (12800000+5280000 x+780000 x^2+40000 x^3+\left (5120000+2112000 x+312000 x^2+16000 x^3\right ) \log (2)+\left (512000+211200 x+31200 x^2+1600 x^3\right ) \log ^2(2)\right ) \log ^3\left (x^2\right )+\left (-6400000-4800000 x-900000 x^2-50000 x^3+\left (-2560000-1920000 x-360000 x^2-20000 x^3\right ) \log (2)+\left (-256000-192000 x-36000 x^2-2000 x^3\right ) \log ^2(2)\right ) \log ^4\left (x^2\right )+\left (31999975+12000000 x+1500000 x^2+62500 x^3+\left (12800000+4800000 x+600000 x^2+25000 x^3\right ) \log (2)+\left (1280000+480000 x+60000 x^2+2500 x^3\right ) \log ^2(2)\right ) \log ^5\left (x^2\right )}{\log ^5\left (x^2\right )} \, dx\\ &=\frac {1}{25} \int \left (25 \left (1279999+512000 \log (2)+51200 \log ^2(2)+19200 x (5+\log (2))^2+2400 x^2 (5+\log (2))^2+100 x^3 (5+\log (2))^2\right )-\frac {8 x^3 (5+\log (2))^2}{\log ^5\left (x^2\right )}+\frac {4 x^2 (240+31 x) (5+\log (2))^2}{\log ^4\left (x^2\right )}-\frac {40 x \left (960+252 x+17 x^2\right ) (5+\log (2))^2}{\log ^3\left (x^2\right )}+\frac {800 \left (640+264 x+39 x^2+2 x^3\right ) (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {2000 (2+x) (8+x)^2 (5+\log (2))^2}{\log \left (x^2\right )}\right ) \, dx\\ &=\frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \frac {x^2 (240+31 x)}{\log ^4\left (x^2\right )} \, dx-\frac {1}{25} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^5\left (x^2\right )} \, dx-\frac {1}{5} \left (8 (5+\log (2))^2\right ) \int \frac {x \left (960+252 x+17 x^2\right )}{\log ^3\left (x^2\right )} \, dx+\left (32 (5+\log (2))^2\right ) \int \frac {640+264 x+39 x^2+2 x^3}{\log ^2\left (x^2\right )} \, dx-\left (80 (5+\log (2))^2\right ) \int \frac {(2+x) (8+x)^2}{\log \left (x^2\right )} \, dx+\int \left (1279999+512000 \log (2)+51200 \log ^2(2)+19200 x (5+\log (2))^2+2400 x^2 (5+\log (2))^2+100 x^3 (5+\log (2))^2\right ) \, dx\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}+\frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \left (\frac {240 x^2}{\log ^4\left (x^2\right )}+\frac {31 x^3}{\log ^4\left (x^2\right )}\right ) \, dx-\frac {1}{25} \left (4 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^4\left (x^2\right )} \, dx-\frac {1}{5} \left (8 (5+\log (2))^2\right ) \int \left (\frac {960 x}{\log ^3\left (x^2\right )}+\frac {252 x^2}{\log ^3\left (x^2\right )}+\frac {17 x^3}{\log ^3\left (x^2\right )}\right ) \, dx+\left (32 (5+\log (2))^2\right ) \int \left (\frac {640}{\log ^2\left (x^2\right )}+\frac {264 x}{\log ^2\left (x^2\right )}+\frac {39 x^2}{\log ^2\left (x^2\right )}+\frac {2 x^3}{\log ^2\left (x^2\right )}\right ) \, dx-\left (80 (5+\log (2))^2\right ) \int \left (\frac {128}{\log \left (x^2\right )}+\frac {96 x}{\log \left (x^2\right )}+\frac {18 x^2}{\log \left (x^2\right )}+\frac {x^3}{\log \left (x^2\right )}\right ) \, dx\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}+\frac {2 x^4 (5+\log (2))^2}{75 \log ^3\left (x^2\right )}-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{25} \left (124 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^4\left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{5} \left (192 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^4\left (x^2\right )} \, dx+\left (64 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx-\left (80 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (2016 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^3\left (x^2\right )} \, dx+\left (1248 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\left (1440 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (1536 (5+\log (2))^2\right ) \int \frac {x}{\log ^3\left (x^2\right )} \, dx-\left (7680 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (8448 (5+\log (2))^2\right ) \int \frac {x}{\log ^2\left (x^2\right )} \, dx-\left (10240 (5+\log (2))^2\right ) \int \frac {1}{\log \left (x^2\right )} \, dx+\left (20480 (5+\log (2))^2\right ) \int \frac {1}{\log ^2\left (x^2\right )} \, dx\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {504 x^3 (5+\log (2))^2}{5 \log ^2\left (x^2\right )}+\frac {512 x^4 (5+\log (2))^2}{75 \log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {4224 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {624 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {32 x^4 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^3\left (x^2\right )} \, dx+\frac {1}{5} \left (96 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^3\left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx-\left (40 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\left (128 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (1512 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\left (768 (5+\log (2))^2\right ) \int \frac {x}{\log ^2\left (x^2\right )} \, dx+\left (1872 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (3840 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+\left (8448 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (10240 (5+\log (2))^2\right ) \int \frac {1}{\log \left (x^2\right )} \, dx-\frac {\left (720 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{3/2}}-\frac {\left (5120 x (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}}\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2-\frac {5120 x \text {Ei}\left (\frac {\log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\sqrt {x^2}}-\frac {720 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\left (x^2\right )^{3/2}}-40 \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {2364 x^3 (5+\log (2))^2}{5 \log \left (x^2\right )}-\frac {1376 x^4 (5+\log (2))^2}{75 \log \left (x^2\right )}-3840 (5+\log (2))^2 \text {li}\left (x^2\right )-\frac {1}{75} \left (16 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \int \frac {x^3}{\log ^2\left (x^2\right )} \, dx+\frac {1}{5} \left (72 (5+\log (2))^2\right ) \int \frac {x^2}{\log ^2\left (x^2\right )} \, dx-\frac {1}{5} \left (272 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\left (64 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )-\frac {1}{5} \left (2268 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\left (768 (5+\log (2))^2\right ) \int \frac {x}{\log \left (x^2\right )} \, dx+\left (4224 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+\frac {\left (936 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\left (x^2\right )^{3/2}}+\frac {\left (5120 x (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}}\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+\frac {216 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{\left (x^2\right )^{3/2}}+24 \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}+384 (5+\log (2))^2 \text {li}\left (x^2\right )-\frac {1}{75} \left (8 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\frac {1}{75} \left (496 (5+\log (2))^2\right ) \int \frac {x^3}{\log \left (x^2\right )} \, dx+\frac {1}{5} \left (108 (5+\log (2))^2\right ) \int \frac {x^2}{\log \left (x^2\right )} \, dx-\frac {1}{5} \left (136 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )-\left (384 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )-\frac {\left (1134 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{5 \left (x^2\right )^{3/2}}\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2-\frac {54 x^3 \text {Ei}\left (\frac {3 \log \left (x^2\right )}{2}\right ) (5+\log (2))^2}{5 \left (x^2\right )^{3/2}}-\frac {248}{75} \text {Ei}\left (2 \log \left (x^2\right )\right ) (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}+\frac {1}{75} \left (248 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log \left (x^2\right )\right )+\frac {\left (54 x^3 (5+\log (2))^2\right ) \text {Subst}\left (\int \frac {e^{3 x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{5 \left (x^2\right )^{3/2}}\\ &=9600 x^2 (5+\log (2))^2+800 x^3 (5+\log (2))^2+25 x^4 (5+\log (2))^2+x \left (1279999+512000 \log (2)+51200 \log ^2(2)\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {32 x^3 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}-\frac {4 x^4 (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {384 x^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {96 x^3 (5+\log (2))^2}{\log ^2\left (x^2\right )}+\frac {6 x^4 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {10240 x (5+\log (2))^2}{\log \left (x^2\right )}-\frac {3840 x^2 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {480 x^3 (5+\log (2))^2}{\log \left (x^2\right )}-\frac {20 x^4 (5+\log (2))^2}{\log \left (x^2\right )}\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(129\) vs. \(2(28)=56\).
time = 0.38, size = 129, normalized size = 4.61 \begin {gather*} x \left (1279999+512000 \log (2)+51200 \log ^2(2)+9600 x (5+\log (2))^2+800 x^2 (5+\log (2))^2+25 x^3 (5+\log (2))^2\right )+\frac {x^4 (5+\log (2))^2}{25 \log ^4\left (x^2\right )}-\frac {4 x^3 (8+x) (5+\log (2))^2}{5 \log ^3\left (x^2\right )}+\frac {6 x^2 (8+x)^2 (5+\log (2))^2}{\log ^2\left (x^2\right )}-\frac {20 x (8+x)^3 (5+\log (2))^2}{\log \left (x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-200*x^3 - 80*x^3*Log[2] - 8*x^3*Log[2]^2 + (24000*x^2 + 3100*x^3 + (9600*x^2 + 1240*x^3)*Log[2] +
(960*x^2 + 124*x^3)*Log[2]^2)*Log[x^2] + (-960000*x - 252000*x^2 - 17000*x^3 + (-384000*x - 100800*x^2 - 6800*
x^3)*Log[2] + (-38400*x - 10080*x^2 - 680*x^3)*Log[2]^2)*Log[x^2]^2 + (12800000 + 5280000*x + 780000*x^2 + 400
00*x^3 + (5120000 + 2112000*x + 312000*x^2 + 16000*x^3)*Log[2] + (512000 + 211200*x + 31200*x^2 + 1600*x^3)*Lo
g[2]^2)*Log[x^2]^3 + (-6400000 - 4800000*x - 900000*x^2 - 50000*x^3 + (-2560000 - 1920000*x - 360000*x^2 - 200
00*x^3)*Log[2] + (-256000 - 192000*x - 36000*x^2 - 2000*x^3)*Log[2]^2)*Log[x^2]^4 + (31999975 + 12000000*x + 1
500000*x^2 + 62500*x^3 + (12800000 + 4800000*x + 600000*x^2 + 25000*x^3)*Log[2] + (1280000 + 480000*x + 60000*
x^2 + 2500*x^3)*Log[2]^2)*Log[x^2]^5)/(25*Log[x^2]^5),x]

[Out]

x*(1279999 + 512000*Log[2] + 51200*Log[2]^2 + 9600*x*(5 + Log[2])^2 + 800*x^2*(5 + Log[2])^2 + 25*x^3*(5 + Log
[2])^2) + (x^4*(5 + Log[2])^2)/(25*Log[x^2]^4) - (4*x^3*(8 + x)*(5 + Log[2])^2)/(5*Log[x^2]^3) + (6*x^2*(8 + x
)^2*(5 + Log[2])^2)/Log[x^2]^2 - (20*x*(8 + x)^3*(5 + Log[2])^2)/Log[x^2]

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(302\) vs. \(2(26)=52\).
time = 159.13, size = 303, normalized size = 10.82

method	result	size
norman	\(\frac {\left (\frac {\ln \left (2\right )^{2}}{25}+\frac {2 \ln \left (2\right )}{5}+1\right ) x^{4}+\left (-10240 \ln \left (2\right )^{2}-102400 \ln \left (2\right )-256000\right ) x \ln \left (x^{2}\right )^{3}+\left (-3840 \ln \left (2\right )^{2}-38400 \ln \left (2\right )-96000\right ) x^{2} \ln \left (x^{2}\right )^{3}+\left (-480 \ln \left (2\right )^{2}-4800 \ln \left (2\right )-12000\right ) x^{3} \ln \left (x^{2}\right )^{3}+\left (-20 \ln \left (2\right )^{2}-200 \ln \left (2\right )-500\right ) x^{4} \ln \left (x^{2}\right )^{3}+\left (6 \ln \left (2\right )^{2}+60 \ln \left (2\right )+150\right ) x^{4} \ln \left (x^{2}\right )^{2}+\left (25 \ln \left (2\right )^{2}+250 \ln \left (2\right )+625\right ) x^{4} \ln \left (x^{2}\right )^{4}+\left (96 \ln \left (2\right )^{2}+960 \ln \left (2\right )+2400\right ) x^{3} \ln \left (x^{2}\right )^{2}+\left (384 \ln \left (2\right )^{2}+3840 \ln \left (2\right )+9600\right ) x^{2} \ln \left (x^{2}\right )^{2}+\left (800 \ln \left (2\right )^{2}+8000 \ln \left (2\right )+20000\right ) x^{3} \ln \left (x^{2}\right )^{4}+\left (9600 \ln \left (2\right )^{2}+96000 \ln \left (2\right )+240000\right ) x^{2} \ln \left (x^{2}\right )^{4}+\left (51200 \ln \left (2\right )^{2}+512000 \ln \left (2\right )+1279999\right ) x \ln \left (x^{2}\right )^{4}+\left (-\frac {32 \ln \left (2\right )^{2}}{5}-64 \ln \left (2\right )-160\right ) x^{3} \ln \left (x^{2}\right )+\left (-\frac {4 \ln \left (2\right )^{2}}{5}-8 \ln \left (2\right )-20\right ) x^{4} \ln \left (x^{2}\right )}{\ln \left (x^{2}\right )^{4}}\)	\(303\)
risch	\(25 x^{4} \ln \left (2\right )^{2}+800 x^{3} \ln \left (2\right )^{2}+250 x^{4} \ln \left (2\right )+9600 x^{2} \ln \left (2\right )^{2}+8000 x^{3} \ln \left (2\right )+625 x^{4}+51200 x \ln \left (2\right )^{2}+96000 x^{2} \ln \left (2\right )+20000 x^{3}+512000 x \ln \left (2\right )+240000 x^{2}+1279999 x -\frac {x \left (-150 x^{3} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}-2400 x^{2} \ln \left (2\right )^{2} \ln \left (x^{2}\right )^{2}+300000 x^{2} \ln \left (x^{2}\right )^{3}-3750 x^{3} \ln \left (x^{2}\right )^{2}+500 x^{3} \ln \left (x^{2}\right )-x^{3} \ln \left (2\right )^{2}-10 x^{3} \ln \left (2\right )+2400000 x \ln \left (x^{2}\right )^{3}+6400000 \ln \left (x^{2}\right )^{3}-60000 x^{2} \ln \left (x^{2}\right )^{2}-240000 x \ln \left (x^{2}\right )^{2}+4000 x^{2} \ln \left (x^{2}\right )-25 x^{3}+12500 \ln \left (x^{2}\right )^{3} x^{3}+256000 \ln \left (x^{2}\right )^{3} \ln \left (2\right )^{2}+2560000 \ln \left (x^{2}\right )^{3} \ln \left (2\right )+500 \ln \left (x^{2}\right )^{3} \ln \left (2\right )^{2} x^{3}+12000 \ln \left (x^{2}\right )^{3} \ln \left (2\right )^{2} x^{2}+5000 \ln \left (x^{2}\right )^{3} \ln \left (2\right ) x^{3}+96000 \ln \left (x^{2}\right )^{3} \ln \left (2\right )^{2} x +120000 \ln \left (x^{2}\right )^{3} \ln \left (2\right ) x^{2}-1500 \ln \left (x^{2}\right )^{2} \ln \left (2\right ) x^{3}+20 \ln \left (x^{2}\right ) \ln \left (2\right )^{2} x^{3}+960000 \ln \left (x^{2}\right )^{3} \ln \left (2\right ) x -9600 \ln \left (x^{2}\right )^{2} \ln \left (2\right )^{2} x -24000 \ln \left (x^{2}\right )^{2} \ln \left (2\right ) x^{2}+160 \ln \left (x^{2}\right ) \ln \left (2\right )^{2} x^{2}+200 \ln \left (x^{2}\right ) \ln \left (2\right ) x^{3}-96000 \ln \left (x^{2}\right )^{2} \ln \left (2\right ) x +1600 \ln \left (x^{2}\right ) \ln \left (2\right ) x^{2}\right )}{25 \ln \left (x^{2}\right )^{4}}\)	\(429\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*ln(2)^2+(25000*x^3+600000*x^2+4800000*x+12800000)*ln(2)+62500
*x^3+1500000*x^2+12000000*x+31999975)*ln(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*ln(2)^2+(-20000*x^3-360
000*x^2-1920000*x-2560000)*ln(2)-50000*x^3-900000*x^2-4800000*x-6400000)*ln(x^2)^4+((1600*x^3+31200*x^2+211200
*x+512000)*ln(2)^2+(16000*x^3+312000*x^2+2112000*x+5120000)*ln(2)+40000*x^3+780000*x^2+5280000*x+12800000)*ln(
x^2)^3+((-680*x^3-10080*x^2-38400*x)*ln(2)^2+(-6800*x^3-100800*x^2-384000*x)*ln(2)-17000*x^3-252000*x^2-960000
*x)*ln(x^2)^2+((124*x^3+960*x^2)*ln(2)^2+(1240*x^3+9600*x^2)*ln(2)+3100*x^3+24000*x^2)*ln(x^2)-8*x^3*ln(2)^2-8
0*x^3*ln(2)-200*x^3)/ln(x^2)^5,x,method=_RETURNVERBOSE)

[Out]

((1/25*ln(2)^2+2/5*ln(2)+1)*x^4+(-10240*ln(2)^2-102400*ln(2)-256000)*x*ln(x^2)^3+(-3840*ln(2)^2-38400*ln(2)-96
000)*x^2*ln(x^2)^3+(-480*ln(2)^2-4800*ln(2)-12000)*x^3*ln(x^2)^3+(-20*ln(2)^2-200*ln(2)-500)*x^4*ln(x^2)^3+(6*
ln(2)^2+60*ln(2)+150)*x^4*ln(x^2)^2+(25*ln(2)^2+250*ln(2)+625)*x^4*ln(x^2)^4+(96*ln(2)^2+960*ln(2)+2400)*x^3*l
n(x^2)^2+(384*ln(2)^2+3840*ln(2)+9600)*x^2*ln(x^2)^2+(800*ln(2)^2+8000*ln(2)+20000)*x^3*ln(x^2)^4+(9600*ln(2)^
2+96000*ln(2)+240000)*x^2*ln(x^2)^4+(51200*ln(2)^2+512000*ln(2)+1279999)*x*ln(x^2)^4+(-32/5*ln(2)^2-64*ln(2)-1
60)*x^3*ln(x^2)+(-4/5*ln(2)^2-8*ln(2)-20)*x^4*ln(x^2))/ln(x^2)^4

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 249 vs. \(2 (28) = 56\).
time = 0.51, size = 249, normalized size = 8.89 \begin {gather*} 25 \, x^{4} \log \left (2\right )^{2} + 250 \, x^{4} \log \left (2\right ) + 800 \, x^{3} \log \left (2\right )^{2} + 625 \, x^{4} + 8000 \, x^{3} \log \left (2\right ) + 9600 \, x^{2} \log \left (2\right )^{2} + 20000 \, x^{3} + 96000 \, x^{2} \log \left (2\right ) + 51200 \, x \log \left (2\right )^{2} + 240000 \, x^{2} + 512000 \, x \log \left (2\right ) + 1279999 \, x + \frac {{\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} - 4000 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 24 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 192 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2} + 512 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x\right )} \log \left (x\right )^{3} + 600 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 16 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 64 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2}\right )} \log \left (x\right )^{2} - 40 \, {\left ({\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 8 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3}\right )} \log \left (x\right )}{400 \, \log \left (x\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3+600000*x^2+4800000*x+12800000)*log(
2)+62500*x^3+1500000*x^2+12000000*x+31999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-200
00*x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6400000)*log(x^2)^4+((1600*x^3+3120
0*x^2+211200*x+512000)*log(2)^2+(16000*x^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x
[phone])*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800*x^2-384000*x)*log(2)-17000*x^3-
252000*x^2-960000*x)*log(x^2)^2+((124*x^3+960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log
(x^2)-8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm="maxima")

[Out]

25*x^4*log(2)^2 + 250*x^4*log(2) + 800*x^3*log(2)^2 + 625*x^4 + 8000*x^3*log(2) + 9600*x^2*log(2)^2 + 20000*x^
3 + 96000*x^2*log(2) + 51200*x*log(2)^2 + 240000*x^2 + 512000*x*log(2) + 1279999*x + 1/400*((log(2)^2 + 10*log
(2) + 25)*x^4 - 4000*((log(2)^2 + 10*log(2) + 25)*x^4 + 24*(log(2)^2 + 10*log(2) + 25)*x^3 + 192*(log(2)^2 + 1
0*log(2) + 25)*x^2 + 512*(log(2)^2 + 10*log(2) + 25)*x)*log(x)^3 + 600*((log(2)^2 + 10*log(2) + 25)*x^4 + 16*(
log(2)^2 + 10*log(2) + 25)*x^3 + 64*(log(2)^2 + 10*log(2) + 25)*x^2)*log(x)^2 - 40*((log(2)^2 + 10*log(2) + 25
)*x^4 + 8*(log(2)^2 + 10*log(2) + 25)*x^3)*log(x))/log(x)^4

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 275 vs. \(2 (28) = 56\).
time = 0.44, size = 275, normalized size = 9.82 \begin {gather*} \frac {x^{4} \log \left (2\right )^{2} + 10 \, x^{4} \log \left (2\right ) + 25 \, {\left (625 \, x^{4} + 20000 \, x^{3} + 25 \, {\left (x^{4} + 32 \, x^{3} + 384 \, x^{2} + 2048 \, x\right )} \log \left (2\right )^{2} + 240000 \, x^{2} + 250 \, {\left (x^{4} + 32 \, x^{3} + 384 \, x^{2} + 2048 \, x\right )} \log \left (2\right ) + 1279999 \, x\right )} \log \left (x^{2}\right )^{4} + 25 \, x^{4} - 500 \, {\left (25 \, x^{4} + 600 \, x^{3} + {\left (x^{4} + 24 \, x^{3} + 192 \, x^{2} + 512 \, x\right )} \log \left (2\right )^{2} + 4800 \, x^{2} + 10 \, {\left (x^{4} + 24 \, x^{3} + 192 \, x^{2} + 512 \, x\right )} \log \left (2\right ) + 12800 \, x\right )} \log \left (x^{2}\right )^{3} + 150 \, {\left (25 \, x^{4} + 400 \, x^{3} + {\left (x^{4} + 16 \, x^{3} + 64 \, x^{2}\right )} \log \left (2\right )^{2} + 1600 \, x^{2} + 10 \, {\left (x^{4} + 16 \, x^{3} + 64 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (x^{2}\right )^{2} - 20 \, {\left (25 \, x^{4} + 200 \, x^{3} + {\left (x^{4} + 8 \, x^{3}\right )} \log \left (2\right )^{2} + 10 \, {\left (x^{4} + 8 \, x^{3}\right )} \log \left (2\right )\right )} \log \left (x^{2}\right )}{25 \, \log \left (x^{2}\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3+600000*x^2+4800000*x+12800000)*log(
2)+62500*x^3+1500000*x^2+12000000*x+31999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-200
00*x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6400000)*log(x^2)^4+((1600*x^3+3120
0*x^2+211200*x+512000)*log(2)^2+(16000*x^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x
[phone])*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800*x^2-384000*x)*log(2)-17000*x^3-
252000*x^2-960000*x)*log(x^2)^2+((124*x^3+960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log
(x^2)-8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm="fricas")

[Out]

1/25*(x^4*log(2)^2 + 10*x^4*log(2) + 25*(625*x^4 + 20000*x^3 + 25*(x^4 + 32*x^3 + 384*x^2 + 2048*x)*log(2)^2 +
240000*x^2 + 250*(x^4 + 32*x^3 + 384*x^2 + 2048*x)*log(2) + 1279999*x)*log(x^2)^4 + 25*x^4 - 500*(25*x^4 + 60
0*x^3 + (x^4 + 24*x^3 + 192*x^2 + 512*x)*log(2)^2 + 4800*x^2 + 10*(x^4 + 24*x^3 + 192*x^2 + 512*x)*log(2) + 12
800*x)*log(x^2)^3 + 150*(25*x^4 + 400*x^3 + (x^4 + 16*x^3 + 64*x^2)*log(2)^2 + 1600*x^2 + 10*(x^4 + 16*x^3 + 6
4*x^2)*log(2))*log(x^2)^2 - 20*(25*x^4 + 200*x^3 + (x^4 + 8*x^3)*log(2)^2 + 10*(x^4 + 8*x^3)*log(2))*log(x^2))
/log(x^2)^4

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 326 vs. \(2 (22) = 44\).
time = 0.19, size = 326, normalized size = 11.64 \begin {gather*} x^{4} \cdot \left (25 \log {\left (2 \right )}^{2} + 250 \log {\left (2 \right )} + 625\right ) + x^{3} \cdot \left (800 \log {\left (2 \right )}^{2} + 8000 \log {\left (2 \right )} + 20000\right ) + x^{2} \cdot \left (9600 \log {\left (2 \right )}^{2} + 96000 \log {\left (2 \right )} + 240000\right ) + x \left (51200 \log {\left (2 \right )}^{2} + 512000 \log {\left (2 \right )} + 1279999\right ) + \frac {x^{4} \log {\left (2 \right )}^{2} + 10 x^{4} \log {\left (2 \right )} + 25 x^{4} + \left (- 500 x^{4} - 200 x^{4} \log {\left (2 \right )} - 20 x^{4} \log {\left (2 \right )}^{2} - 4000 x^{3} - 1600 x^{3} \log {\left (2 \right )} - 160 x^{3} \log {\left (2 \right )}^{2}\right ) \log {\left (x^{2} \right )} + \left (150 x^{4} \log {\left (2 \right )}^{2} + 1500 x^{4} \log {\left (2 \right )} + 3750 x^{4} + 2400 x^{3} \log {\left (2 \right )}^{2} + 24000 x^{3} \log {\left (2 \right )} + 60000 x^{3} + 9600 x^{2} \log {\left (2 \right )}^{2} + 96000 x^{2} \log {\left (2 \right )} + 240000 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (- 12500 x^{4} - 5000 x^{4} \log {\left (2 \right )} - 500 x^{4} \log {\left (2 \right )}^{2} - 300000 x^{3} - 120000 x^{3} \log {\left (2 \right )} - 12000 x^{3} \log {\left (2 \right )}^{2} - 2400000 x^{2} - 960000 x^{2} \log {\left (2 \right )} - 96000 x^{2} \log {\left (2 \right )}^{2} - 6400000 x - 2560000 x \log {\left (2 \right )} - 256000 x \log {\left (2 \right )}^{2}\right ) \log {\left (x^{2} \right )}^{3}}{25 \log {\left (x^{2} \right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((2500*x**3+60000*x**2+480000*x+1280000)*ln(2)**2+(25000*x**3+600000*x**2+4800000*x+12800000)*
ln(2)+62500*x**3+1500000*x**2+12000000*x+31999975)*ln(x**2)**5+((-2000*x**3-36000*x**2-192000*x-256000)*ln(2)*
*2+(-20000*x**3-360000*x**2-1920000*x-2560000)*ln(2)-50000*x**3-900000*x**2-4800000*x-6400000)*ln(x**2)**4+((1
600*x**3+31200*x**2+211200*x+512000)*ln(2)**2+(16000*x**3+312000*x**2+2112000*x+5120000)*ln(2)+40000*x**3+7800
00*x**2+5280000*x+12800000)*ln(x**2)**3+((-680*x**3-10080*x**2-38400*x)*ln(2)**2+(-6800*x**3-100800*x**2-38400
0*x)*ln(2)-17000*x**3-252000*x**2-960000*x)*ln(x**2)**2+((124*x**3+960*x**2)*ln(2)**2+(1240*x**3+9600*x**2)*ln
(2)+3100*x**3+24000*x**2)*ln(x**2)-8*x**3*ln(2)**2-80*x**3*ln(2)-200*x**3)/ln(x**2)**5,x)

[Out]

x**4*(25*log(2)**2 + 250*log(2) + 625) + x**3*(800*log(2)**2 + 8000*log(2) + 20000) + x**2*(9600*log(2)**2 + 9
6000*log(2) + 240000) + x*(51200*log(2)**2 + 512000*log(2) + 1279999) + (x**4*log(2)**2 + 10*x**4*log(2) + 25*
x**4 + (-500*x**4 - 200*x**4*log(2) - 20*x**4*log(2)**2 - 4000*x**3 - 1600*x**3*log(2) - 160*x**3*log(2)**2)*l
og(x**2) + (150*x**4*log(2)**2 + 1500*x**4*log(2) + 3750*x**4 + 2400*x**3*log(2)**2 + 24000*x**3*log(2) + 6000
0*x**3 + 9600*x**2*log(2)**2 + 96000*x**2*log(2) + 240000*x**2)*log(x**2)**2 + (-12500*x**4 - 5000*x**4*log(2)
- 500*x**4*log(2)**2 - 300000*x**3 - 120000*x**3*log(2) - 12000*x**3*log(2)**2 - 2400000*x**2 - 960000*x**2*l
og(2) - 96000*x**2*log(2)**2 - 6400000*x - 2560000*x*log(2) - 256000*x*log(2)**2)*log(x**2)**3)/(25*log(x**2)*
*4)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 423 vs. \(2 (28) = 56\).
time = 0.57, size = 423, normalized size = 15.11 \begin {gather*} 25 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{4} + 800 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{3} + 9600 \, {\left (\log \left (2\right )^{2} + 10 \, \log \left (2\right ) + 25\right )} x^{2} + {\left (51200 \, \log \left (2\right )^{2} + 512000 \, \log \left (2\right ) + 1279999\right )} x - \frac {500 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - 150 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 5000 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 12000 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} + 20 \, x^{4} \log \left (2\right )^{2} \log \left (x^{2}\right ) - 1500 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right )^{2} - 2400 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 12500 \, x^{4} \log \left (x^{2}\right )^{3} + 120000 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 96000 \, x^{2} \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - x^{4} \log \left (2\right )^{2} + 200 \, x^{4} \log \left (2\right ) \log \left (x^{2}\right ) + 160 \, x^{3} \log \left (2\right )^{2} \log \left (x^{2}\right ) - 3750 \, x^{4} \log \left (x^{2}\right )^{2} - 24000 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right )^{2} - 9600 \, x^{2} \log \left (2\right )^{2} \log \left (x^{2}\right )^{2} + 300000 \, x^{3} \log \left (x^{2}\right )^{3} + 960000 \, x^{2} \log \left (2\right ) \log \left (x^{2}\right )^{3} + 256000 \, x \log \left (2\right )^{2} \log \left (x^{2}\right )^{3} - 10 \, x^{4} \log \left (2\right ) + 500 \, x^{4} \log \left (x^{2}\right ) + 1600 \, x^{3} \log \left (2\right ) \log \left (x^{2}\right ) - 60000 \, x^{3} \log \left (x^{2}\right )^{2} - 96000 \, x^{2} \log \left (2\right ) \log \left (x^{2}\right )^{2} + 2400000 \, x^{2} \log \left (x^{2}\right )^{3} + 2560000 \, x \log \left (2\right ) \log \left (x^{2}\right )^{3} - 25 \, x^{4} + 4000 \, x^{3} \log \left (x^{2}\right ) - 240000 \, x^{2} \log \left (x^{2}\right )^{2} + 6400000 \, x \log \left (x^{2}\right )^{3}}{25 \, \log \left (x^{2}\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(((2500*x^3+60000*x^2+480000*x+1280000)*log(2)^2+(25000*x^3+600000*x^2+4800000*x+12800000)*log(
2)+62500*x^3+1500000*x^2+12000000*x+31999975)*log(x^2)^5+((-2000*x^3-36000*x^2-192000*x-256000)*log(2)^2+(-200
00*x^3-360000*x^2-1920000*x-2560000)*log(2)-50000*x^3-900000*x^2-4800000*x-6400000)*log(x^2)^4+((1600*x^3+3120
0*x^2+211200*x+512000)*log(2)^2+(16000*x^3+312000*x^2+2112000*x+5120000)*log(2)+40000*x^3+780000*x^2+5280000*x
[phone])*log(x^2)^3+((-680*x^3-10080*x^2-38400*x)*log(2)^2+(-6800*x^3-100800*x^2-384000*x)*log(2)-17000*x^3-
252000*x^2-960000*x)*log(x^2)^2+((124*x^3+960*x^2)*log(2)^2+(1240*x^3+9600*x^2)*log(2)+3100*x^3+24000*x^2)*log
(x^2)-8*x^3*log(2)^2-80*x^3*log(2)-200*x^3)/log(x^2)^5,x, algorithm="giac")

[Out]

25*(log(2)^2 + 10*log(2) + 25)*x^4 + 800*(log(2)^2 + 10*log(2) + 25)*x^3 + 9600*(log(2)^2 + 10*log(2) + 25)*x^
2 + (51200*log(2)^2 + 512000*log(2) + 1279999)*x - 1/25*(500*x^4*log(2)^2*log(x^2)^3 - 150*x^4*log(2)^2*log(x^
2)^2 + 5000*x^4*log(2)*log(x^2)^3 + 12000*x^3*log(2)^2*log(x^2)^3 + 20*x^4*log(2)^2*log(x^2) - 1500*x^4*log(2)
*log(x^2)^2 - 2400*x^3*log(2)^2*log(x^2)^2 + 12500*x^4*log(x^2)^3 + 120000*x^3*log(2)*log(x^2)^3 + 96000*x^2*l
og(2)^2*log(x^2)^3 - x^4*log(2)^2 + 200*x^4*log(2)*log(x^2) + 160*x^3*log(2)^2*log(x^2) - 3750*x^4*log(x^2)^2
- 24000*x^3*log(2)*log(x^2)^2 - 9600*x^2*log(2)^2*log(x^2)^2 + 300000*x^3*log(x^2)^3 + 960000*x^2*log(2)*log(x
^2)^3 + 256000*x*log(2)^2*log(x^2)^3 - 10*x^4*log(2) + 500*x^4*log(x^2) + 1600*x^3*log(2)*log(x^2) - 60000*x^3
*log(x^2)^2 - 96000*x^2*log(2)*log(x^2)^2 + 2400000*x^2*log(x^2)^3 + 2560000*x*log(2)*log(x^2)^3 - 25*x^4 + 40
00*x^3*log(x^2) - 240000*x^2*log(x^2)^2 + 6400000*x*log(x^2)^3)/log(x^2)^4

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Mupad [B]
time = 2.36, size = 205, normalized size = 7.32 \begin {gather*} \frac {9600\,x^3\,{\left (\ln \left (2\right )+5\right )}^2+800\,x^4\,{\left (\ln \left (2\right )+5\right )}^2+25\,x^5\,{\left (\ln \left (2\right )+5\right )}^2+\frac {x^2\,\left (12800000\,\ln \left (2\right )+1280000\,{\ln \left (2\right )}^2+31999975\right )}{25}}{x}+\frac {\frac {x^5\,\left (10\,\ln \left (2\right )+{\ln \left (2\right )}^2+25\right )}{25}+{\ln \left (x^2\right )}^2\,\left (6\,{\left (\ln \left (2\right )+5\right )}^2\,x^5+96\,{\left (\ln \left (2\right )+5\right )}^2\,x^4+384\,{\left (\ln \left (2\right )+5\right )}^2\,x^3\right )-\ln \left (x^2\right )\,\left (\frac {4\,{\left (\ln \left (2\right )+5\right )}^2\,x^5}{5}+\frac {32\,{\left (\ln \left (2\right )+5\right )}^2\,x^4}{5}\right )-{\ln \left (x^2\right )}^3\,\left (20\,{\left (\ln \left (2\right )+5\right )}^2\,x^5+480\,{\left (\ln \left (2\right )+5\right )}^2\,x^4+3840\,{\left (\ln \left (2\right )+5\right )}^2\,x^3+10240\,{\left (\ln \left (2\right )+5\right )}^2\,x^2\right )}{x\,{\ln \left (x^2\right )}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((8*x^3*log(2)^2)/25 - (log(x^2)*(log(2)*(9600*x^2 + 1240*x^3) + 24000*x^2 + 3100*x^3 + log(2)^2*(960*x^2
+ 124*x^3)))/25 + (16*x^3*log(2))/5 + 8*x^3 + (log(x^2)^2*(960000*x + log(2)*(384000*x + 100800*x^2 + 6800*x^
3) + log(2)^2*(38400*x + 10080*x^2 + 680*x^3) + 252000*x^2 + 17000*x^3))/25 + (log(x^2)^4*(4800000*x + log(2)*
(1920000*x + 360000*x^2 + 20000*x^3 + 2560000) + log(2)^2*(192000*x + 36000*x^2 + 2000*x^3 + 256000) + 900000*
x^2 + 50000*x^3 + 6400000))/25 - (log(x^2)^3*(5280000*x + log(2)*(2112000*x + 312000*x^2 + 16000*x^3 + 5120000
) + log(2)^2*(211200*x + 31200*x^2 + 1600*x^3 + 512000) + 780000*x^2 + 40000*x^3 + 12800000))/25 - (log(x^2)^5
*(12000000*x + log(2)*(4800000*x + 600000*x^2 + 25000*x^3 + 12800000) + log(2)^2*(480000*x + 60000*x^2 + 2500*
x^3 + 1280000) + 1500000*x^2 + 62500*x^3 + 31999975))/25)/log(x^2)^5,x)

[Out]

(9600*x^3*(log(2) + 5)^2 + 800*x^4*(log(2) + 5)^2 + 25*x^5*(log(2) + 5)^2 + (x^2*(12800000*log(2) + 1280000*lo
g(2)^2 + 31999975))/25)/x + ((x^5*(10*log(2) + log(2)^2 + 25))/25 + log(x^2)^2*(384*x^3*(log(2) + 5)^2 + 96*x^
4*(log(2) + 5)^2 + 6*x^5*(log(2) + 5)^2) - log(x^2)*((32*x^4*(log(2) + 5)^2)/5 + (4*x^5*(log(2) + 5)^2)/5) - l
og(x^2)^3*(10240*x^2*(log(2) + 5)^2 + 3840*x^3*(log(2) + 5)^2 + 480*x^4*(log(2) + 5)^2 + 20*x^5*(log(2) + 5)^2
))/(x*log(x^2)^4)

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