\(\int \frac {432 x^2-492 x^3+552 x^4+168 x^5+(576 x^2-984 x^3-252 x^4) \log (x^2)+(432 x^2+84 x^3) \log ^2(x^2)}{576+336 x+49 x^2} \, dx\) [2123]

Optimal result

Integrand size = 73, antiderivative size = 27 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {x^3 \left (-1-\left (-x+\log \left (x^2\right )\right )^2\right )}{-4-\frac {7 x}{6}} \]

[Out]

(-1-(ln(x^2)-x)^2)*x^3/(-7/6*x-4)

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(127\) vs. \(2(27)=54\).

Time = 0.47 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.70, number of steps used = 31, number of rules used = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.205, Rules used = {27, 6873, 12, 6874, 45, 2404, 2332, 2341, 2351, 31, 2354, 2438, 2333, 2342, 2355} \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6 x^4}{7}-\frac {144 x^3}{49}+\frac {3750 x^2}{343}+\frac {6}{7} x^2 \log ^2\left (x^2\right )+\frac {3456 x \log ^2\left (x^2\right )}{49 (7 x+24)}-\frac {144}{49} x \log ^2\left (x^2\right )+\frac {288}{49} x^2 \log \left (x^2\right )+\frac {165888 x \log \left (x^2\right )}{343 (7 x+24)}-\frac {6912}{343} x \log \left (x^2\right )-\frac {12}{7} x^3 \log \left (x^2\right )-\frac {90000 x}{2401}-\frac {51840000}{16807 (7 x+24)} \]

[In]

Int[(432*x^2 - 492*x^3 + 552*x^4 + 168*x^5 + (576*x^2 - 984*x^3 - 252*x^4)*Log[x^2] + (432*x^2 + 84*x^3)*Log[x
^2]^2)/(576 + 336*x + 49*x^2),x]

[Out]

(-90000*x)/2401 + (3750*x^2)/343 - (144*x^3)/49 + (6*x^4)/7 - 51840000/(16807*(24 + 7*x)) - (6912*x*Log[x^2])/
343 + (288*x^2*Log[x^2])/49 - (12*x^3*Log[x^2])/7 + (165888*x*Log[x^2])/(343*(24 + 7*x)) - (144*x*Log[x^2]^2)/
49 + (6*x^2*Log[x^2]^2)/7 + (3456*x*Log[x^2]^2)/(49*(24 + 7*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 27

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

Rule 31

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

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2333

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

Rule 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2342

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Lo
g[c*x^n])^p/(d*(m + 1))), x] - Dist[b*n*(p/(m + 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] && GtQ[p, 0]

Rule 2351

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 2354

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 2355

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 2404

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 2438

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 6873

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

Rule 6874

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{(24+7 x)^2} \, dx \\ & = \int \frac {12 x^2 \left (36-41 x+46 x^2+14 x^3+48 \log \left (x^2\right )-82 x \log \left (x^2\right )-21 x^2 \log \left (x^2\right )+36 \log ^2\left (x^2\right )+7 x \log ^2\left (x^2\right )\right )}{(24+7 x)^2} \, dx \\ & = 12 \int \frac {x^2 \left (36-41 x+46 x^2+14 x^3+48 \log \left (x^2\right )-82 x \log \left (x^2\right )-21 x^2 \log \left (x^2\right )+36 \log ^2\left (x^2\right )+7 x \log ^2\left (x^2\right )\right )}{(24+7 x)^2} \, dx \\ & = 12 \int \left (\frac {36 x^2}{(24+7 x)^2}-\frac {41 x^3}{(24+7 x)^2}+\frac {46 x^4}{(24+7 x)^2}+\frac {14 x^5}{(24+7 x)^2}-\frac {x^2 \left (-48+82 x+21 x^2\right ) \log \left (x^2\right )}{(24+7 x)^2}+\frac {x^2 (36+7 x) \log ^2\left (x^2\right )}{(24+7 x)^2}\right ) \, dx \\ & = -\left (12 \int \frac {x^2 \left (-48+82 x+21 x^2\right ) \log \left (x^2\right )}{(24+7 x)^2} \, dx\right )+12 \int \frac {x^2 (36+7 x) \log ^2\left (x^2\right )}{(24+7 x)^2} \, dx+168 \int \frac {x^5}{(24+7 x)^2} \, dx+432 \int \frac {x^2}{(24+7 x)^2} \, dx-492 \int \frac {x^3}{(24+7 x)^2} \, dx+552 \int \frac {x^4}{(24+7 x)^2} \, dx \\ & = -\left (12 \int \left (\frac {912 \log \left (x^2\right )}{343}-\frac {62}{49} x \log \left (x^2\right )+\frac {3}{7} x^2 \log \left (x^2\right )-\frac {331776 \log \left (x^2\right )}{343 (24+7 x)^2}-\frac {1152 \log \left (x^2\right )}{49 (24+7 x)}\right ) \, dx\right )+12 \int \left (-\frac {12}{49} \log ^2\left (x^2\right )+\frac {1}{7} x \log ^2\left (x^2\right )+\frac {6912 \log ^2\left (x^2\right )}{49 (24+7 x)^2}\right ) \, dx+168 \int \left (-\frac {55296}{16807}+\frac {1728 x}{2401}-\frac {48 x^2}{343}+\frac {x^3}{49}-\frac {7962624}{16807 (24+7 x)^2}+\frac {1658880}{16807 (24+7 x)}\right ) \, dx+432 \int \left (\frac {1}{49}+\frac {576}{49 (24+7 x)^2}-\frac {48}{49 (24+7 x)}\right ) \, dx-492 \int \left (-\frac {48}{343}+\frac {x}{49}-\frac {13824}{343 (24+7 x)^2}+\frac {1728}{343 (24+7 x)}\right ) \, dx+552 \int \left (\frac {1728}{2401}-\frac {48 x}{343}+\frac {x^2}{49}+\frac {331776}{2401 (24+7 x)^2}-\frac {55296}{2401 (24+7 x)}\right ) \, dx \\ & = -\frac {186768 x}{2401}+\frac {5766 x^2}{343}-\frac {200 x^3}{49}+\frac {6 x^4}{7}-\frac {51840000}{16807 (24+7 x)}+\frac {331776 \log (24+7 x)}{2401}+\frac {12}{7} \int x \log ^2\left (x^2\right ) \, dx-\frac {144}{49} \int \log ^2\left (x^2\right ) \, dx-\frac {36}{7} \int x^2 \log \left (x^2\right ) \, dx+\frac {744}{49} \int x \log \left (x^2\right ) \, dx-\frac {10944}{343} \int \log \left (x^2\right ) \, dx+\frac {13824}{49} \int \frac {\log \left (x^2\right )}{24+7 x} \, dx+\frac {82944}{49} \int \frac {\log ^2\left (x^2\right )}{(24+7 x)^2} \, dx+\frac {3981312}{343} \int \frac {\log \left (x^2\right )}{(24+7 x)^2} \, dx \\ & = -\frac {33552 x}{2401}+\frac {3162 x^2}{343}-\frac {144 x^3}{49}+\frac {6 x^4}{7}-\frac {51840000}{16807 (24+7 x)}-\frac {10944}{343} x \log \left (x^2\right )+\frac {372}{49} x^2 \log \left (x^2\right )-\frac {12}{7} x^3 \log \left (x^2\right )+\frac {165888 x \log \left (x^2\right )}{343 (24+7 x)}+\frac {13824}{343} \log \left (1+\frac {7 x}{24}\right ) \log \left (x^2\right )-\frac {144}{49} x \log ^2\left (x^2\right )+\frac {6}{7} x^2 \log ^2\left (x^2\right )+\frac {3456 x \log ^2\left (x^2\right )}{49 (24+7 x)}+\frac {331776 \log (24+7 x)}{2401}-\frac {24}{7} \int x \log \left (x^2\right ) \, dx+\frac {576}{49} \int \log \left (x^2\right ) \, dx-\frac {27648}{343} \int \frac {\log \left (1+\frac {7 x}{24}\right )}{x} \, dx-\frac {13824}{49} \int \frac {\log \left (x^2\right )}{24+7 x} \, dx-\frac {331776}{343} \int \frac {1}{24+7 x} \, dx \\ & = -\frac {90000 x}{2401}+\frac {3750 x^2}{343}-\frac {144 x^3}{49}+\frac {6 x^4}{7}-\frac {51840000}{16807 (24+7 x)}-\frac {6912}{343} x \log \left (x^2\right )+\frac {288}{49} x^2 \log \left (x^2\right )-\frac {12}{7} x^3 \log \left (x^2\right )+\frac {165888 x \log \left (x^2\right )}{343 (24+7 x)}-\frac {144}{49} x \log ^2\left (x^2\right )+\frac {6}{7} x^2 \log ^2\left (x^2\right )+\frac {3456 x \log ^2\left (x^2\right )}{49 (24+7 x)}+\frac {27648}{343} \operatorname {PolyLog}\left (2,-\frac {7 x}{24}\right )+\frac {27648}{343} \int \frac {\log \left (1+\frac {7 x}{24}\right )}{x} \, dx \\ & = -\frac {90000 x}{2401}+\frac {3750 x^2}{343}-\frac {144 x^3}{49}+\frac {6 x^4}{7}-\frac {51840000}{16807 (24+7 x)}-\frac {6912}{343} x \log \left (x^2\right )+\frac {288}{49} x^2 \log \left (x^2\right )-\frac {12}{7} x^3 \log \left (x^2\right )+\frac {165888 x \log \left (x^2\right )}{343 (24+7 x)}-\frac {144}{49} x \log ^2\left (x^2\right )+\frac {6}{7} x^2 \log ^2\left (x^2\right )+\frac {3456 x \log ^2\left (x^2\right )}{49 (24+7 x)} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(71\) vs. \(2(27)=54\).

Time = 0.14 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.63 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6 \left (-8640000-2520000 x+16807 x^3+16807 x^5-9289728 \log (24)-2709504 x \log (24)+387072 (24+7 x) \log (x)-14 \left (331776+96768 x+2401 x^4\right ) \log \left (x^2\right )+16807 x^3 \log ^2\left (x^2\right )\right )}{16807 (24+7 x)} \]

[In]

Integrate[(432*x^2 - 492*x^3 + 552*x^4 + 168*x^5 + (576*x^2 - 984*x^3 - 252*x^4)*Log[x^2] + (432*x^2 + 84*x^3)
*Log[x^2]^2)/(576 + 336*x + 49*x^2),x]

[Out]

(6*(-8640000 - 2520000*x + 16807*x^3 + 16807*x^5 - 9289728*Log[24] - 2709504*x*Log[24] + 387072*(24 + 7*x)*Log
[x] - 14*(331776 + 96768*x + 2401*x^4)*Log[x^2] + 16807*x^3*Log[x^2]^2))/(16807*(24 + 7*x))

Maple [A] (verified)

Time = 0.36 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.48

method	result	size
norman	\(\frac {6 x^{3}+6 x^{5}+6 x^{3} \ln \left (x^{2}\right )^{2}-12 x^{4} \ln \left (x^{2}\right )}{7 x +24}\)	\(40\)
parallelrisch	\(\frac {84 x^{5}-168 x^{4} \ln \left (x^{2}\right )+84 x^{3} \ln \left (x^{2}\right )^{2}+84 x^{3}}{98 x +336}\)	\(41\)

[In]

int(((84*x^3+432*x^2)*ln(x^2)^2+(-252*x^4-984*x^3+576*x^2)*ln(x^2)+168*x^5+552*x^4-492*x^3+432*x^2)/(49*x^2+33
6*x+576),x,method=_RETURNVERBOSE)

[Out]

(6*x^3+6*x^5+6*x^3*ln(x^2)^2-12*x^4*ln(x^2))/(7*x+24)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.63 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6 \, {\left (16807 \, x^{5} - 33614 \, x^{4} \log \left (x^{2}\right ) + 16807 \, x^{3} \log \left (x^{2}\right )^{2} + 16807 \, x^{3} - 2520000 \, x - 8640000\right )}}{16807 \, {\left (7 \, x + 24\right )}} \]

[In]

integrate(((84*x^3+432*x^2)*log(x^2)^2+(-252*x^4-984*x^3+576*x^2)*log(x^2)+168*x^5+552*x^4-492*x^3+432*x^2)/(4
9*x^2+336*x+576),x, algorithm="fricas")

[Out]

6/16807*(16807*x^5 - 33614*x^4*log(x^2) + 16807*x^3*log(x^2)^2 + 16807*x^3 - 2520000*x - 8640000)/(7*x + 24)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (22) = 44\).

Time = 0.20 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.81 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6 x^{4}}{7} - \frac {144 x^{3}}{49} + \frac {6 x^{3} \log {\left (x^{2} \right )}^{2}}{7 x + 24} + \frac {3750 x^{2}}{343} - \frac {90000 x}{2401} + \frac {331776 \log {\left (x \right )}}{2401} - \frac {51840000}{117649 x + 403368} + \frac {\left (- 28812 x^{4} - 1161216 x - 3981312\right ) \log {\left (x^{2} \right )}}{16807 x + 57624} \]

[In]

integrate(((84*x**3+432*x**2)*ln(x**2)**2+(-252*x**4-984*x**3+576*x**2)*ln(x**2)+168*x**5+552*x**4-492*x**3+43
2*x**2)/(49*x**2+336*x+576),x)

[Out]

6*x**4/7 - 144*x**3/49 + 6*x**3*log(x**2)**2/(7*x + 24) + 3750*x**2/343 - 90000*x/2401 + 331776*log(x)/2401 -
51840000/(117649*x + 403368) + (-28812*x**4 - 1161216*x - 3981312)*log(x**2)/(16807*x + 57624)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).

Time = 0.22 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.07 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6}{7} \, x^{4} - \frac {200}{49} \, x^{3} + \frac {5766}{343} \, x^{2} - \frac {186768}{2401} \, x + \frac {8 \, {\left (7203 \, x^{3} \log \left (x\right )^{2} + 2401 \, x^{4} - 4116 \, x^{3} + 42336 \, x^{2} - 3 \, {\left (2401 \, x^{4} + 96768 \, x + 331776\right )} \log \left (x\right ) + 290304 \, x\right )}}{2401 \, {\left (7 \, x + 24\right )}} - \frac {51840000}{16807 \, {\left (7 \, x + 24\right )}} + \frac {331776}{2401} \, \log \left (x\right ) \]

[In]

integrate(((84*x^3+432*x^2)*log(x^2)^2+(-252*x^4-984*x^3+576*x^2)*log(x^2)+168*x^5+552*x^4-492*x^3+432*x^2)/(4
9*x^2+336*x+576),x, algorithm="maxima")

[Out]

6/7*x^4 - 200/49*x^3 + 5766/343*x^2 - 186768/2401*x + 8/2401*(7203*x^3*log(x)^2 + 2401*x^4 - 4116*x^3 + 42336*
x^2 - 3*(2401*x^4 + 96768*x + 331776)*log(x) + 290304*x)/(7*x + 24) - 51840000/16807/(7*x + 24) + 331776/2401*
log(x)

Giac [F]

\[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\int { \frac {12 \, {\left (14 \, x^{5} + 46 \, x^{4} - 41 \, x^{3} + {\left (7 \, x^{3} + 36 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 36 \, x^{2} - {\left (21 \, x^{4} + 82 \, x^{3} - 48 \, x^{2}\right )} \log \left (x^{2}\right )\right )}}{49 \, x^{2} + 336 \, x + 576} \,d x } \]

[In]

integrate(((84*x^3+432*x^2)*log(x^2)^2+(-252*x^4-984*x^3+576*x^2)*log(x^2)+168*x^5+552*x^4-492*x^3+432*x^2)/(4
9*x^2+336*x+576),x, algorithm="giac")

[Out]

integrate(12*(14*x^5 + 46*x^4 - 41*x^3 + (7*x^3 + 36*x^2)*log(x^2)^2 + 36*x^2 - (21*x^4 + 82*x^3 - 48*x^2)*log
(x^2))/(49*x^2 + 336*x + 576), x)

Mupad [B] (verification not implemented)

Time = 10.50 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {432 x^2-492 x^3+552 x^4+168 x^5+\left (576 x^2-984 x^3-252 x^4\right ) \log \left (x^2\right )+\left (432 x^2+84 x^3\right ) \log ^2\left (x^2\right )}{576+336 x+49 x^2} \, dx=\frac {6\,x^5-12\,x^4\,\ln \left (x^2\right )+6\,x^3\,{\ln \left (x^2\right )}^2+6\,x^3}{7\,x+24} \]

[In]

int((log(x^2)^2*(432*x^2 + 84*x^3) - log(x^2)*(984*x^3 - 576*x^2 + 252*x^4) + 432*x^2 - 492*x^3 + 552*x^4 + 16
8*x^5)/(336*x + 49*x^2 + 576),x)

[Out]

(6*x^3 - 12*x^4*log(x^2) + 6*x^5 + 6*x^3*log(x^2)^2)/(7*x + 24)