3.88.95 \(\int \frac {10 x}{125-75 x+15 x^2-x^3+(600 x-240 x^2+24 x^3) (i \pi +\log (\frac {e}{4}))^2+(960 x^2-192 x^3) (i \pi +\log (\frac {e}{4}))^4+512 x^3 (i \pi +\log (\frac {e}{4}))^6} \, dx\) [8795]

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

[Out]

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

________________________________________________________________________________________

Rubi [B] Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(133\) vs. \(2(28)=56\).
time = 0.56, antiderivative size = 133, normalized size of antiderivative = 4.75, number of steps used = 4, number of rules used = 3, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6, 12, 2099} \begin {gather*} \frac {25}{\left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )^2 \left (5+x \left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )\right )^2}-\frac {10}{\left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )^2 \left (5+x \left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(10*x)/(125 - 75*x + 15*x^2 - x^3 + (600*x - 240*x^2 + 24*x^3)*(I*Pi + Log[E/4])^2 + (960*x^2 - 192*x^3)*(
I*Pi + Log[E/4])^4 + 512*x^3*(I*Pi + Log[E/4])^6),x]

[Out]

25/((7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^2)^2*(5 + x*(7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4
]) - 16*Log[4] + 8*Log[4]^2))^2) - 10/((7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^2)^2*(5 + x
*(7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^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 2099

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 x}{125-75 x+15 x^2+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+x^3 \left (-1+512 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6\right )} \, dx\\ &=10 \int \frac {x}{125-75 x+15 x^2+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+x^3 \left (-1+512 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6\right )} \, dx\\ &=10 \int \left (\frac {5}{\left (-7+8 \pi ^2-16 i \pi (1-\log (4))+16 \log (4)-8 \log ^2(4)\right ) \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^3}+\frac {1}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right ) \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^2}\right ) \, dx\\ &=\frac {25}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )^2 \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^2}-\frac {10}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )^2 \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B] Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(28)=56\).
time = 0.07, size = 93, normalized size = 3.32 \begin {gather*} -\frac {5 \left (5-2 x \left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )\right )}{\left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )^2 \left (-5+x \left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*x)/(125 - 75*x + 15*x^2 - x^3 + (600*x - 240*x^2 + 24*x^3)*(I*Pi + Log[E/4])^2 + (960*x^2 - 192*
x^3)*(I*Pi + Log[E/4])^4 + 512*x^3*(I*Pi + Log[E/4])^6),x]

[Out]

(-5*(5 - 2*x*(-7 + 8*Pi^2 + (16*I)*Pi*(-1 + Log[4]) + 16*Log[4] - 8*Log[4]^2)))/((-7 + 8*Pi^2 + (16*I)*Pi*(-1
+ Log[4]) + 16*Log[4] - 8*Log[4]^2)^2*(-5 + x*(-7 + 8*Pi^2 + (16*I)*Pi*(-1 + Log[4]) + 16*Log[4] - 8*Log[4]^2)
)^2)

________________________________________________________________________________________

Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(21)=42\).
time = 15.24, size = 66, normalized size = 2.36

method	result	size
default	\(-\frac {10}{\left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2} \left (8 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+5-x \right )}+\frac {25}{\left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2} \left (8 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+5-x \right )^{2}}\)	\(66\)
gosper	\(-\frac {5 \left (16 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-2 x +5\right )}{\left (64 \ln \left (-\frac {{\mathrm e}}{4}\right )^{4} x^{2}-16 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2} x^{2}+80 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+x^{2}-10 x +25\right ) \left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2}}\)	\(75\)
risch	\(\frac {-\frac {5 x}{512 \left (7-32 i \ln \left (2\right ) \pi -8 \pi ^{2}+16 i \pi +32 \ln \left (2\right )^{2}-32 \ln \left (2\right )\right )}-\frac {25}{1024 \left (7-32 i \ln \left (2\right ) \pi -8 \pi ^{2}+16 i \pi +32 \ln \left (2\right )^{2}-32 \ln \left (2\right )\right )^{2}}}{-2 i \ln \left (2\right )^{3} \pi \,x^{2}-\frac {5 i \ln \left (2\right ) \pi x}{16}+x^{2} \ln \left (2\right )^{4}-\frac {3 \pi ^{2} \ln \left (2\right )^{2} x^{2}}{2}-\frac {23 i \ln \left (2\right ) \pi \,x^{2}}{16}+\frac {\pi ^{4} x^{2}}{16}+\frac {i \ln \left (2\right ) \pi ^{3} x^{2}}{2}-2 x^{2} \ln \left (2\right )^{3}+\frac {3 \pi ^{2} \ln \left (2\right ) x^{2}}{2}+3 i \ln \left (2\right )^{2} \pi \,x^{2}+\frac {23 x^{2} \ln \left (2\right )^{2}}{16}+\frac {5 i x \pi }{32}-\frac {23 \pi ^{2} x^{2}}{64}+\frac {7 i \pi \,x^{2}}{32}+\frac {5 x \ln \left (2\right )^{2}}{16}-\frac {7 x^{2} \ln \left (2\right )}{16}-\frac {5 x \,\pi ^{2}}{64}-\frac {i \pi ^{3} x^{2}}{4}-\frac {5 x \ln \left (2\right )}{16}+\frac {49 x^{2}}{1024}+\frac {35 x}{512}+\frac {25}{1024}}\)	\(238\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x/(512*x^3*ln(-1/4*exp(1))^6+(-192*x^3+960*x^2)*ln(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*ln(-1/4*exp(1)
)^2-x^3+15*x^2-75*x+125),x,method=_RETURNVERBOSE)

[Out]

-10/(8*ln(-1/4*exp(1))^2-1)^2/(8*x*ln(-1/4*exp(1))^2+5-x)+25/(8*ln(-1/4*exp(1))^2-1)^2/(8*x*ln(-1/4*exp(1))^2+
5-x)^2

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (21) = 42\).
time = 0.26, size = 114, normalized size = 4.07 \begin {gather*} -\frac {5 \, {\left (2 \, {\left (8 \, \log \left (-\frac {1}{4} \, e\right )^{2} - 1\right )} x + 5\right )}}{1600 \, \log \left (-\frac {1}{4} \, e\right )^{4} + {\left (4096 \, \log \left (-\frac {1}{4} \, e\right )^{8} - 2048 \, \log \left (-\frac {1}{4} \, e\right )^{6} + 384 \, \log \left (-\frac {1}{4} \, e\right )^{4} - 32 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 1\right )} x^{2} + 10 \, {\left (512 \, \log \left (-\frac {1}{4} \, e\right )^{6} - 192 \, \log \left (-\frac {1}{4} \, e\right )^{4} + 24 \, \log \left (-\frac {1}{4} \, e\right )^{2} - 1\right )} x - 400 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="maxima")

[Out]

-5*(2*(8*log(-1/4*e)^2 - 1)*x + 5)/(1600*log(-1/4*e)^4 + (4096*log(-1/4*e)^8 - 2048*log(-1/4*e)^6 + 384*log(-1
/4*e)^4 - 32*log(-1/4*e)^2 + 1)*x^2 + 10*(512*log(-1/4*e)^6 - 192*log(-1/4*e)^4 + 24*log(-1/4*e)^2 - 1)*x - 40
0*log(-1/4*e)^2 + 25)

________________________________________________________________________________________

Fricas [C] Result contains complex when optimal does not.
time = 0.35, size = 199, normalized size = 7.11 \begin {gather*} -\frac {5 \, {\left (16 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} x - 32 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )} x + 14 \, x + 5\right )}}{4096 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{8} x^{2} - 32768 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{7} x^{2} + 5120 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{6} {\left (22 \, x^{2} + x\right )} - 2048 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{5} {\left (106 \, x^{2} + 15 \, x\right )} + 64 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{4} {\left (4006 \, x^{2} + 1170 \, x + 25\right )} - 256 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{3} {\left (742 \, x^{2} + 370 \, x + 25\right )} + 80 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} {\left (1078 \, x^{2} + 819 \, x + 115\right )} - 224 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )} {\left (98 \, x^{2} + 105 \, x + 25\right )} + 2401 \, x^{2} + 3430 \, x + 1225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="fricas")

[Out]

-5*(16*(I*pi + 2*log(2))^2*x - 32*(I*pi + 2*log(2))*x + 14*x + 5)/(4096*(I*pi + 2*log(2))^8*x^2 - 32768*(I*pi
+ 2*log(2))^7*x^2 + 5120*(I*pi + 2*log(2))^6*(22*x^2 + x) - 2048*(I*pi + 2*log(2))^5*(106*x^2 + 15*x) + 64*(I*
pi + 2*log(2))^4*(4006*x^2 + 1170*x + 25) - 256*(I*pi + 2*log(2))^3*(742*x^2 + 370*x + 25) + 80*(I*pi + 2*log(
2))^2*(1078*x^2 + 819*x + 115) - 224*(I*pi + 2*log(2))*(98*x^2 + 105*x + 25) + 2401*x^2 + 3430*x + 1225)

________________________________________________________________________________________

Sympy [B] Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 765 vs. \(2 (22) = 44\).
time = 5.25, size = 765, normalized size = 27.32 \begin {gather*} - \frac {10 \left (x \left (- 16 \pi ^{2} - 64 \log {\left (2 \right )} + 14 + 64 \log {\left (2 \right )}^{2} - 64 i \pi \log {\left (2 \right )} + 32 i \pi \right ) + 5\right )}{x^{2} \left (- 18350080 \pi ^{4} \log {\left (2 \right )}^{3} - 917504 \pi ^{6} \log {\left (2 \right )}^{2} - 4341760 \pi ^{4} \log {\left (2 \right )} - 225280 \pi ^{6} - 54067200 \pi ^{2} \log {\left (2 \right )}^{4} - 12306432 \pi ^{2} \log {\left (2 \right )}^{2} - 14680064 \pi ^{2} \log {\left (2 \right )}^{6} - 13893632 \log {\left (2 \right )}^{5} - 172480 \pi ^{2} - 3039232 \log {\left (2 \right )}^{3} - 8388608 \log {\left (2 \right )}^{7} - 87808 \log {\left (2 \right )} + 4802 + 2097152 \log {\left (2 \right )}^{8} + 689920 \log {\left (2 \right )}^{2} + 14417920 \log {\left (2 \right )}^{6} + 8204288 \log {\left (2 \right )}^{4} + 2279424 \pi ^{2} \log {\left (2 \right )} + 512768 \pi ^{4} + 44040192 \pi ^{2} \log {\left (2 \right )}^{5} + 8192 \pi ^{8} + 34734080 \pi ^{2} \log {\left (2 \right )}^{3} + 9175040 \pi ^{4} \log {\left (2 \right )}^{4} + 917504 \pi ^{6} \log {\left (2 \right )} + 13516800 \pi ^{4} \log {\left (2 \right )}^{2} - 2703360 i \pi ^{5} \log {\left (2 \right )} - 3670016 i \pi ^{5} \log {\left (2 \right )}^{3} - 36700160 i \pi ^{3} \log {\left (2 \right )}^{4} - 17367040 i \pi ^{3} \log {\left (2 \right )}^{2} - 65536 i \pi ^{7} - 43253760 i \pi \log {\left (2 \right )}^{5} - 16408576 i \pi \log {\left (2 \right )}^{3} - 379904 i \pi ^{3} - 8388608 i \pi \log {\left (2 \right )}^{7} - 689920 i \pi \log {\left (2 \right )} + 43904 i \pi + 4558848 i \pi \log {\left (2 \right )}^{2} + 29360128 i \pi \log {\left (2 \right )}^{6} + 34734080 i \pi \log {\left (2 \right )}^{4} + 14680064 i \pi ^{3} \log {\left (2 \right )}^{5} + 4102144 i \pi ^{3} \log {\left (2 \right )} + 434176 i \pi ^{5} + 131072 i \pi ^{7} \log {\left (2 \right )} + 36044800 i \pi ^{3} \log {\left (2 \right )}^{3} + 5505024 i \pi ^{5} \log {\left (2 \right )}^{2}\right ) + x \left (- 614400 \pi ^{4} \log {\left (2 \right )} - 3594240 \pi ^{2} \log {\left (2 \right )}^{2} - 10240 \pi ^{6} - 2457600 \pi ^{2} \log {\left (2 \right )}^{4} - 131040 \pi ^{2} - 1515520 \log {\left (2 \right )}^{3} - 1966080 \log {\left (2 \right )}^{5} - 94080 \log {\left (2 \right )} + 6860 + 655360 \log {\left (2 \right )}^{6} + 524160 \log {\left (2 \right )}^{2} + 2396160 \log {\left (2 \right )}^{4} + 1136640 \pi ^{2} \log {\left (2 \right )} + 149760 \pi ^{4} + 4915200 \pi ^{2} \log {\left (2 \right )}^{3} + 614400 \pi ^{4} \log {\left (2 \right )}^{2} - 2457600 i \pi ^{3} \log {\left (2 \right )}^{2} - 122880 i \pi ^{5} \log {\left (2 \right )} - 189440 i \pi ^{3} - 4792320 i \pi \log {\left (2 \right )}^{3} - 524160 i \pi \log {\left (2 \right )} - 1966080 i \pi \log {\left (2 \right )}^{5} + 47040 i \pi + 2273280 i \pi \log {\left (2 \right )}^{2} + 4915200 i \pi \log {\left (2 \right )}^{4} + 1638400 i \pi ^{3} \log {\left (2 \right )}^{3} + 61440 i \pi ^{5} + 1198080 i \pi ^{3} \log {\left (2 \right )}\right ) - 76800 \pi ^{2} \log {\left (2 \right )}^{2} - 18400 \pi ^{2} - 102400 \log {\left (2 \right )}^{3} - 22400 \log {\left (2 \right )} + 2450 + 51200 \log {\left (2 \right )}^{4} + 73600 \log {\left (2 \right )}^{2} + 3200 \pi ^{4} + 76800 \pi ^{2} \log {\left (2 \right )} - 12800 i \pi ^{3} - 73600 i \pi \log {\left (2 \right )} - 102400 i \pi \log {\left (2 \right )}^{3} + 11200 i \pi + 153600 i \pi \log {\left (2 \right )}^{2} + 25600 i \pi ^{3} \log {\left (2 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/(512*x**3*ln(-1/4*exp(1))**6+(-192*x**3+960*x**2)*ln(-1/4*exp(1))**4+(24*x**3-240*x**2+600*x)*l
n(-1/4*exp(1))**2-x**3+15*x**2-75*x+125),x)

[Out]

-10*(x*(-16*pi**2 - 64*log(2) + 14 + 64*log(2)**2 - 64*I*pi*log(2) + 32*I*pi) + 5)/(x**2*(-18350080*pi**4*log(
2)**3 - 917504*pi**6*log(2)**2 - 4341760*pi**4*log(2) - 225280*pi**6 - 54067200*pi**2*log(2)**4 - 12306432*pi*
*2*log(2)**2 - 14680064*pi**2*log(2)**6 - 13893632*log(2)**5 - 172480*pi**2 - 3039232*log(2)**3 - 8388608*log(
2)**7 - 87808*log(2) + 4802 + 2097152*log(2)**8 + 689920*log(2)**2 + 14417920*log(2)**6 + 8204288*log(2)**4 +
2279424*pi**2*log(2) + 512768*pi**4 + 44040192*pi**2*log(2)**5 + 8192*pi**8 + 34734080*pi**2*log(2)**3 + 91750
40*pi**4*log(2)**4 + 917504*pi**6*log(2) + 13516800*pi**4*log(2)**2 - 2703360*I*pi**5*log(2) - 3670016*I*pi**5
*log(2)**3 - 36700160*I*pi**3*log(2)**4 - 17367040*I*pi**3*log(2)**2 - 65536*I*pi**7 - 43253760*I*pi*log(2)**5
- 16408576*I*pi*log(2)**3 - 379904*I*pi**3 - 8388608*I*pi*log(2)**7 - 689920*I*pi*log(2) + 43904*I*pi + 45588
48*I*pi*log(2)**2 + 29360128*I*pi*log(2)**6 + 34734080*I*pi*log(2)**4 + 14680064*I*pi**3*log(2)**5 + 4102144*I
*pi**3*log(2) + 434176*I*pi**5 + 131072*I*pi**7*log(2) + 36044800*I*pi**3*log(2)**3 + 5505024*I*pi**5*log(2)**
2) + x*(-614400*pi**4*log(2) - 3594240*pi**2*log(2)**2 - 10240*pi**6 - 2457600*pi**2*log(2)**4 - 131040*pi**2
- 1515520*log(2)**3 - 1966080*log(2)**5 - 94080*log(2) + 6860 + 655360*log(2)**6 + 524160*log(2)**2 + 2396160*
log(2)**4 + 1136640*pi**2*log(2) + 149760*pi**4 + 4915200*pi**2*log(2)**3 + 614400*pi**4*log(2)**2 - 2457600*I
*pi**3*log(2)**2 - 122880*I*pi**5*log(2) - 189440*I*pi**3 - 4792320*I*pi*log(2)**3 - 524160*I*pi*log(2) - 1966
080*I*pi*log(2)**5 + 47040*I*pi + 2273280*I*pi*log(2)**2 + 4915200*I*pi*log(2)**4 + 1638400*I*pi**3*log(2)**3
+ 61440*I*pi**5 + 1198080*I*pi**3*log(2)) - 76800*pi**2*log(2)**2 - 18400*pi**2 - 102400*log(2)**3 - 22400*log
(2) + 2450 + 51200*log(2)**4 + 73600*log(2)**2 + 3200*pi**4 + 76800*pi**2*log(2) - 12800*I*pi**3 - 73600*I*pi*
log(2) - 102400*I*pi*log(2)**3 + 11200*I*pi + 153600*I*pi*log(2)**2 + 25600*I*pi**3*log(2))

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (21) = 42\).
time = 0.42, size = 56, normalized size = 2.00 \begin {gather*} -\frac {5 \, {\left (16 \, x \log \left (-\frac {1}{4} \, e\right )^{2} - 2 \, x + 5\right )}}{{\left (64 \, \log \left (-\frac {1}{4} \, e\right )^{4} - 16 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 1\right )} {\left (8 \, x \log \left (-\frac {1}{4} \, e\right )^{2} - x + 5\right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="giac")

[Out]

-5*(16*x*log(-1/4*e)^2 - 2*x + 5)/((64*log(-1/4*e)^4 - 16*log(-1/4*e)^2 + 1)*(8*x*log(-1/4*e)^2 - x + 5)^2)

________________________________________________________________________________________

Mupad [B]
time = 0.20, size = 47, normalized size = 1.68 \begin {gather*} -\frac {5\,\left (16\,x\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-2\,x+5\right )}{{\left (8\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-1\right )}^2\,{\left (8\,x\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-x+5\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x)/(log(-exp(1)/4)^2*(600*x - 240*x^2 + 24*x^3) - 75*x + log(-exp(1)/4)^4*(960*x^2 - 192*x^3) + 512*x^
3*log(-exp(1)/4)^6 + 15*x^2 - x^3 + 125),x)

[Out]

-(5*(16*x*log(-exp(1)/4)^2 - 2*x + 5))/((8*log(-exp(1)/4)^2 - 1)^2*(8*x*log(-exp(1)/4)^2 - x + 5)^2)

________________________________________________________________________________________