3.4.88 \(\int \frac {(18400 x+160 x^2+800 x^3) \log (x^4)+(4600 x+20 x^2) \log ^2(x^4)}{13225+230 x+1151 x^2+10 x^3+25 x^4} \, dx\)

Optimal. Leaf size=23 \[ \frac {4 x^2 \log ^2\left (x^4\right )}{23+\frac {x}{5}+x^2} \]

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Rubi [C]  time = 2.54, antiderivative size = 525, normalized size of antiderivative = 22.83, number of steps used = 50, number of rules used = 15, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.254, Rules used = {6688, 12, 6742, 634, 618, 204, 628, 2357, 2314, 31, 2317, 2391, 2318, 2374, 6589} \begin {gather*} -\frac {147200 \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )}{2299 \left (1-11 i \sqrt {19}\right )}+\frac {64}{209} \left (209+i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )-\frac {147072 \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )}{2299}-\frac {147200 \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )}{2299 \left (1+11 i \sqrt {19}\right )}+\frac {64}{209} \left (209-i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )-\frac {147072 \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )}{2299}+\frac {46000 x \log ^2\left (x^4\right )}{2299 \left (1-11 i \sqrt {19}\right ) \left (10 x-11 i \sqrt {19}+1\right )}+\frac {45960 x \log ^2\left (x^4\right )}{2299 \left (10 x-11 i \sqrt {19}+1\right )}+\frac {46000 x \log ^2\left (x^4\right )}{2299 \left (1+11 i \sqrt {19}\right ) \left (10 x+11 i \sqrt {19}+1\right )}+\frac {45960 x \log ^2\left (x^4\right )}{2299 \left (10 x+11 i \sqrt {19}+1\right )}-\frac {36800 \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right ) \log \left (x^4\right )}{2299 \left (1-11 i \sqrt {19}\right )}+\frac {16}{209} \left (209+i \sqrt {19}\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right ) \log \left (x^4\right )-\frac {36768 \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right ) \log \left (x^4\right )}{2299}-\frac {36800 \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right ) \log \left (x^4\right )}{2299 \left (1+11 i \sqrt {19}\right )}+\frac {16}{209} \left (209-i \sqrt {19}\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right ) \log \left (x^4\right )-\frac {36768 \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right ) \log \left (x^4\right )}{2299} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((18400*x + 160*x^2 + 800*x^3)*Log[x^4] + (4600*x + 20*x^2)*Log[x^4]^2)/(13225 + 230*x + 1151*x^2 + 10*x^3
+ 25*x^4),x]

[Out]

(45960*x*Log[x^4]^2)/(2299*(1 - (11*I)*Sqrt[19] + 10*x)) + (46000*x*Log[x^4]^2)/(2299*(1 - (11*I)*Sqrt[19])*(1
- (11*I)*Sqrt[19] + 10*x)) + (45960*x*Log[x^4]^2)/(2299*(1 + (11*I)*Sqrt[19] + 10*x)) + (46000*x*Log[x^4]^2)/
(2299*(1 + (11*I)*Sqrt[19])*(1 + (11*I)*Sqrt[19] + 10*x)) - (36768*Log[x^4]*Log[1 + (10*x)/(1 - (11*I)*Sqrt[19
])])/2299 + (16*(209 + I*Sqrt[19])*Log[x^4]*Log[1 + (10*x)/(1 - (11*I)*Sqrt[19])])/209 - (36800*Log[x^4]*Log[1
+ (10*x)/(1 - (11*I)*Sqrt[19])])/(2299*(1 - (11*I)*Sqrt[19])) - (36768*Log[x^4]*Log[1 + (10*x)/(1 + (11*I)*Sq
rt[19])])/2299 + (16*(209 - I*Sqrt[19])*Log[x^4]*Log[1 + (10*x)/(1 + (11*I)*Sqrt[19])])/209 - (36800*Log[x^4]*
Log[1 + (10*x)/(1 + (11*I)*Sqrt[19])])/(2299*(1 + (11*I)*Sqrt[19])) - (147072*PolyLog[2, (-10*x)/(1 - (11*I)*S
qrt[19])])/2299 + (64*(209 + I*Sqrt[19])*PolyLog[2, (-10*x)/(1 - (11*I)*Sqrt[19])])/209 - (147200*PolyLog[2, (
-10*x)/(1 - (11*I)*Sqrt[19])])/(2299*(1 - (11*I)*Sqrt[19])) - (147072*PolyLog[2, (-10*x)/(1 + (11*I)*Sqrt[19])
])/2299 + (64*(209 - I*Sqrt[19])*PolyLog[2, (-10*x)/(1 + (11*I)*Sqrt[19])])/209 - (147200*PolyLog[2, (-10*x)/(
1 + (11*I)*Sqrt[19])])/(2299*(1 + (11*I)*Sqrt[19]))

Rule 12

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

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 204

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 634

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 2314

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_), x_Symbol] :> Simp[(x*(d + e*x^r)^(q
+ 1)*(a + b*Log[c*x^n]))/d, x] - Dist[(b*n)/d, Int[(d + e*x^r)^(q + 1), x], x] /; FreeQ[{a, b, c, d, e, n, q,
r}, x] && EqQ[r*(q + 1) + 1, 0]

Rule 2317

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[(Log[1 + (e*x)/d]*(a +
b*Log[c*x^n])^p)/e, x] - Dist[(b*n*p)/e, Int[(Log[1 + (e*x)/d]*(a + b*Log[c*x^n])^(p - 1))/x, x], x] /; FreeQ[
{a, b, c, d, e, n}, x] && IGtQ[p, 0]

Rule 2318

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_))^2, x_Symbol] :> Simp[(x*(a + b*Log[c*x^n])
^p)/(d*(d + e*x)), x] - Dist[(b*n*p)/d, Int[(a + b*Log[c*x^n])^(p - 1)/(d + e*x), x], x] /; FreeQ[{a, b, c, d,
e, n, p}, x] && GtQ[p, 0]

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rule 2374

Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :> -Sim
p[(PolyLog[2, -(d*f*x^m)]*(a + b*Log[c*x^n])^p)/m, x] + Dist[(b*n*p)/m, Int[(PolyLog[2, -(d*f*x^m)]*(a + b*Log
[c*x^n])^(p - 1))/x, x], x] /; FreeQ[{a, b, c, d, e, f, m, n}, x] && IGtQ[p, 0] && EqQ[d*e, 1]

Rule 2391

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> -Simp[PolyLog[2, -(c*e*x^n)]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

Rule 6589

Int[PolyLog[n_, (c_.)*((a_.) + (b_.)*(x_))^(p_.)]/((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[PolyLog[n + 1, c*(a
+ b*x)^p]/(e*p), x] /; FreeQ[{a, b, c, d, e, n, p}, x] && EqQ[b*d, a*e]

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 {20 x \log \left (x^4\right ) \left (8 \left (115+x+5 x^2\right )+(230+x) \log \left (x^4\right )\right )}{\left (115+x+5 x^2\right )^2} \, dx\\ &=20 \int \frac {x \log \left (x^4\right ) \left (8 \left (115+x+5 x^2\right )+(230+x) \log \left (x^4\right )\right )}{\left (115+x+5 x^2\right )^2} \, dx\\ &=20 \int \left (\frac {8 x \log \left (x^4\right )}{115+x+5 x^2}+\frac {x (230+x) \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2}\right ) \, dx\\ &=20 \int \frac {x (230+x) \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2} \, dx+160 \int \frac {x \log \left (x^4\right )}{115+x+5 x^2} \, dx\\ &=20 \int \left (\frac {(-115+1149 x) \log ^2\left (x^4\right )}{5 \left (115+x+5 x^2\right )^2}+\frac {\log ^2\left (x^4\right )}{5 \left (115+x+5 x^2\right )}\right ) \, dx+160 \int \left (\frac {\left (1+\frac {i}{11 \sqrt {19}}\right ) \log \left (x^4\right )}{1-11 i \sqrt {19}+10 x}+\frac {\left (1-\frac {i}{11 \sqrt {19}}\right ) \log \left (x^4\right )}{1+11 i \sqrt {19}+10 x}\right ) \, dx\\ &=4 \int \frac {(-115+1149 x) \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2} \, dx+4 \int \frac {\log ^2\left (x^4\right )}{115+x+5 x^2} \, dx+\frac {1}{209} \left (160 \left (209-i \sqrt {19}\right )\right ) \int \frac {\log \left (x^4\right )}{1+11 i \sqrt {19}+10 x} \, dx+\frac {1}{209} \left (160 \left (209+i \sqrt {19}\right )\right ) \int \frac {\log \left (x^4\right )}{1-11 i \sqrt {19}+10 x} \, dx\\ &=\frac {16}{209} \left (209+i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )+\frac {16}{209} \left (209-i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )+4 \int \left (\frac {10 i \log ^2\left (x^4\right )}{11 \sqrt {19} \left (-1+11 i \sqrt {19}-10 x\right )}+\frac {10 i \log ^2\left (x^4\right )}{11 \sqrt {19} \left (1+11 i \sqrt {19}+10 x\right )}\right ) \, dx+4 \int \left (-\frac {115 \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2}+\frac {1149 x \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2}\right ) \, dx-\frac {1}{209} \left (64 \left (209-i \sqrt {19}\right )\right ) \int \frac {\log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )}{x} \, dx-\frac {1}{209} \left (64 \left (209+i \sqrt {19}\right )\right ) \int \frac {\log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )}{x} \, dx\\ &=\frac {16}{209} \left (209+i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )+\frac {16}{209} \left (209-i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )+\frac {64}{209} \left (209+i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )+\frac {64}{209} \left (209-i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )-460 \int \frac {\log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2} \, dx+4596 \int \frac {x \log ^2\left (x^4\right )}{\left (115+x+5 x^2\right )^2} \, dx+\frac {(40 i) \int \frac {\log ^2\left (x^4\right )}{-1+11 i \sqrt {19}-10 x} \, dx}{11 \sqrt {19}}+\frac {(40 i) \int \frac {\log ^2\left (x^4\right )}{1+11 i \sqrt {19}+10 x} \, dx}{11 \sqrt {19}}\\ &=\frac {16}{209} \left (209+i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )-\frac {4 i \log ^2\left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {16}{209} \left (209-i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )+\frac {4 i \log ^2\left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {64}{209} \left (209+i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )+\frac {64}{209} \left (209-i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )-460 \int \left (-\frac {100 \log ^2\left (x^4\right )}{2299 \left (-1+11 i \sqrt {19}-10 x\right )^2}+\frac {100 i \log ^2\left (x^4\right )}{25289 \sqrt {19} \left (-1+11 i \sqrt {19}-10 x\right )}-\frac {100 \log ^2\left (x^4\right )}{2299 \left (1+11 i \sqrt {19}+10 x\right )^2}+\frac {100 i \log ^2\left (x^4\right )}{25289 \sqrt {19} \left (1+11 i \sqrt {19}+10 x\right )}\right ) \, dx+4596 \int \left (-\frac {10 \left (-1+11 i \sqrt {19}\right ) \log ^2\left (x^4\right )}{2299 \left (-1+11 i \sqrt {19}-10 x\right )^2}-\frac {10 i \log ^2\left (x^4\right )}{25289 \sqrt {19} \left (-1+11 i \sqrt {19}-10 x\right )}-\frac {10 \left (-1-11 i \sqrt {19}\right ) \log ^2\left (x^4\right )}{2299 \left (1+11 i \sqrt {19}+10 x\right )^2}-\frac {10 i \log ^2\left (x^4\right )}{25289 \sqrt {19} \left (1+11 i \sqrt {19}+10 x\right )}\right ) \, dx+\frac {(32 i) \int \frac {\log \left (x^4\right ) \log \left (1-\frac {10 x}{-1+11 i \sqrt {19}}\right )}{x} \, dx}{11 \sqrt {19}}-\frac {(32 i) \int \frac {\log \left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )}{x} \, dx}{11 \sqrt {19}}\\ &=\frac {16}{209} \left (209+i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )-\frac {4 i \log ^2\left (x^4\right ) \log \left (1+\frac {10 x}{1-11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {16}{209} \left (209-i \sqrt {19}\right ) \log \left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )+\frac {4 i \log ^2\left (x^4\right ) \log \left (1+\frac {10 x}{1+11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {64}{209} \left (209+i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )-\frac {32 i \log \left (x^4\right ) \text {Li}_2\left (-\frac {10 x}{1-11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {64}{209} \left (209-i \sqrt {19}\right ) \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )+\frac {32 i \log \left (x^4\right ) \text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )}{11 \sqrt {19}}+\frac {46000 \int \frac {\log ^2\left (x^4\right )}{\left (-1+11 i \sqrt {19}-10 x\right )^2} \, dx}{2299}+\frac {46000 \int \frac {\log ^2\left (x^4\right )}{\left (1+11 i \sqrt {19}+10 x\right )^2} \, dx}{2299}-\frac {(45960 i) \int \frac {\log ^2\left (x^4\right )}{-1+11 i \sqrt {19}-10 x} \, dx}{25289 \sqrt {19}}-\frac {(45960 i) \int \frac {\log ^2\left (x^4\right )}{1+11 i \sqrt {19}+10 x} \, dx}{25289 \sqrt {19}}-\frac {(46000 i) \int \frac {\log ^2\left (x^4\right )}{-1+11 i \sqrt {19}-10 x} \, dx}{25289 \sqrt {19}}-\frac {(46000 i) \int \frac {\log ^2\left (x^4\right )}{1+11 i \sqrt {19}+10 x} \, dx}{25289 \sqrt {19}}+\frac {(128 i) \int \frac {\text {Li}_2\left (\frac {10 x}{-1+11 i \sqrt {19}}\right )}{x} \, dx}{11 \sqrt {19}}-\frac {(128 i) \int \frac {\text {Li}_2\left (-\frac {10 x}{1+11 i \sqrt {19}}\right )}{x} \, dx}{11 \sqrt {19}}+\frac {\left (45960 \left (1-11 i \sqrt {19}\right )\right ) \int \frac {\log ^2\left (x^4\right )}{\left (-1+11 i \sqrt {19}-10 x\right )^2} \, dx}{2299}+\frac {\left (45960 \left (1+11 i \sqrt {19}\right )\right ) \int \frac {\log ^2\left (x^4\right )}{\left (1+11 i \sqrt {19}+10 x\right )^2} \, dx}{2299}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.47, size = 21, normalized size = 0.91 \begin {gather*} \frac {20 x^2 \log ^2\left (x^4\right )}{115+x+5 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((18400*x + 160*x^2 + 800*x^3)*Log[x^4] + (4600*x + 20*x^2)*Log[x^4]^2)/(13225 + 230*x + 1151*x^2 +
10*x^3 + 25*x^4),x]

[Out]

(20*x^2*Log[x^4]^2)/(115 + x + 5*x^2)

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fricas [A]  time = 0.69, size = 21, normalized size = 0.91 \begin {gather*} \frac {20 \, x^{2} \log \left (x^{4}\right )^{2}}{5 \, x^{2} + x + 115} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x^2+4600*x)*log(x^4)^2+(800*x^3+160*x^2+18400*x)*log(x^4))/(25*x^4+10*x^3+1151*x^2+230*x+13225)
,x, algorithm="fricas")

[Out]

20*x^2*log(x^4)^2/(5*x^2 + x + 115)

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giac [A]  time = 0.66, size = 24, normalized size = 1.04 \begin {gather*} -4 \, {\left (\frac {x + 115}{5 \, x^{2} + x + 115} - 1\right )} \log \left (x^{4}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x^2+4600*x)*log(x^4)^2+(800*x^3+160*x^2+18400*x)*log(x^4))/(25*x^4+10*x^3+1151*x^2+230*x+13225)
,x, algorithm="giac")

[Out]

-4*((x + 115)/(5*x^2 + x + 115) - 1)*log(x^4)^2

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maple [A]  time = 0.19, size = 22, normalized size = 0.96

method	result	size
norman	\(\frac {20 \ln \left (x^{4}\right )^{2} x^{2}}{5 x^{2}+x +115}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((20*x^2+4600*x)*ln(x^4)^2+(800*x^3+160*x^2+18400*x)*ln(x^4))/(25*x^4+10*x^3+1151*x^2+230*x+13225),x,metho
d=_RETURNVERBOSE)

[Out]

20*ln(x^4)^2*x^2/(5*x^2+x+115)

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maxima [A]  time = 1.04, size = 19, normalized size = 0.83 \begin {gather*} \frac {320 \, x^{2} \log \relax (x)^{2}}{5 \, x^{2} + x + 115} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x^2+4600*x)*log(x^4)^2+(800*x^3+160*x^2+18400*x)*log(x^4))/(25*x^4+10*x^3+1151*x^2+230*x+13225)
,x, algorithm="maxima")

[Out]

320*x^2*log(x)^2/(5*x^2 + x + 115)

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mupad [B]  time = 0.51, size = 21, normalized size = 0.91 \begin {gather*} \frac {20\,x^2\,{\ln \left (x^4\right )}^2}{5\,x^2+x+115} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x^4)*(18400*x + 160*x^2 + 800*x^3) + log(x^4)^2*(4600*x + 20*x^2))/(230*x + 1151*x^2 + 10*x^3 + 25*x^
4 + 13225),x)

[Out]

(20*x^2*log(x^4)^2)/(x + 5*x^2 + 115)

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sympy [A]  time = 0.18, size = 19, normalized size = 0.83 \begin {gather*} \frac {20 x^{2} \log {\left (x^{4} \right )}^{2}}{5 x^{2} + x + 115} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x**2+4600*x)*ln(x**4)**2+(800*x**3+160*x**2+18400*x)*ln(x**4))/(25*x**4+10*x**3+1151*x**2+230*x
+13225),x)

[Out]

20*x**2*log(x**4)**2/(5*x**2 + x + 115)

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