3.37.55 \(\int \frac {1}{625} (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+(1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5) \log (x)+(100 x+510 x^2+1008 x^3+480 x^4) \log ^2(x)+(64 x^2+64 x^3) \log ^3(x)+3 x^2 \log ^4(x)) \, dx\)

Optimal. Leaf size=23 \[ \frac {\left (x+\left (x+\frac {1}{5} x (4 x+\log (x))\right )^2\right )^2}{x} \]

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Rubi [B]  time = 0.33, antiderivative size = 164, normalized size of antiderivative = 7.13, number of steps used = 32, number of rules used = 6, integrand size = 110, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {12, 2356, 2304, 2305, 1593, 2353} \begin {gather*} \frac {256 x^7}{625}+\frac {256 x^6}{125}+\frac {256}{625} x^6 \log (x)+\frac {96 x^5}{25}+\frac {96}{625} x^5 \log ^2(x)+\frac {192}{125} x^5 \log (x)+\frac {112 x^4}{25}+\frac {16}{625} x^4 \log ^3(x)+\frac {48}{125} x^4 \log ^2(x)+\frac {48}{25} x^4 \log (x)+\frac {21 x^3}{5}+\frac {1}{625} x^3 \log ^4(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {6}{25} x^3 \log ^2(x)+\frac {36}{25} x^3 \log (x)+2 x^2+\frac {2}{25} x^2 \log ^2(x)+\frac {4}{5} x^2 \log (x)+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(625 + 3000*x + 8775*x^2 + 12400*x^3 + 12960*x^4 + 7936*x^5 + 1792*x^6 + (1100*x + 3000*x^2 + 5280*x^3 + 4
992*x^4 + 1536*x^5)*Log[x] + (100*x + 510*x^2 + 1008*x^3 + 480*x^4)*Log[x]^2 + (64*x^2 + 64*x^3)*Log[x]^3 + 3*
x^2*Log[x]^4)/625,x]

[Out]

x + 2*x^2 + (21*x^3)/5 + (112*x^4)/25 + (96*x^5)/25 + (256*x^6)/125 + (256*x^7)/625 + (4*x^2*Log[x])/5 + (36*x
^3*Log[x])/25 + (48*x^4*Log[x])/25 + (192*x^5*Log[x])/125 + (256*x^6*Log[x])/625 + (2*x^2*Log[x]^2)/25 + (6*x^
3*Log[x]^2)/25 + (48*x^4*Log[x]^2)/125 + (96*x^5*Log[x]^2)/625 + (4*x^3*Log[x]^3)/125 + (16*x^4*Log[x]^3)/625
+ (x^3*Log[x]^4)/625

Rule 12

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

Rule 1593

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

Rule 2304

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 2305

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 2353

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 2356

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]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \left (625+3000 x+8775 x^2+12400 x^3+12960 x^4+7936 x^5+1792 x^6+\left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x)+\left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x)+\left (64 x^2+64 x^3\right ) \log ^3(x)+3 x^2 \log ^4(x)\right ) \, dx\\ &=x+\frac {12 x^2}{5}+\frac {117 x^3}{25}+\frac {124 x^4}{25}+\frac {2592 x^5}{625}+\frac {3968 x^6}{1875}+\frac {256 x^7}{625}+\frac {1}{625} \int \left (1100 x+3000 x^2+5280 x^3+4992 x^4+1536 x^5\right ) \log (x) \, dx+\frac {1}{625} \int \left (100 x+510 x^2+1008 x^3+480 x^4\right ) \log ^2(x) \, dx+\frac {1}{625} \int \left (64 x^2+64 x^3\right ) \log ^3(x) \, dx+\frac {3}{625} \int x^2 \log ^4(x) \, dx\\ &=x+\frac {12 x^2}{5}+\frac {117 x^3}{25}+\frac {124 x^4}{25}+\frac {2592 x^5}{625}+\frac {3968 x^6}{1875}+\frac {256 x^7}{625}+\frac {1}{625} x^3 \log ^4(x)+\frac {1}{625} \int x^2 (64+64 x) \log ^3(x) \, dx+\frac {1}{625} \int \left (1100 x \log (x)+3000 x^2 \log (x)+5280 x^3 \log (x)+4992 x^4 \log (x)+1536 x^5 \log (x)\right ) \, dx+\frac {1}{625} \int \left (100 x \log ^2(x)+510 x^2 \log ^2(x)+1008 x^3 \log ^2(x)+480 x^4 \log ^2(x)\right ) \, dx-\frac {4}{625} \int x^2 \log ^3(x) \, dx\\ &=x+\frac {12 x^2}{5}+\frac {117 x^3}{25}+\frac {124 x^4}{25}+\frac {2592 x^5}{625}+\frac {3968 x^6}{1875}+\frac {256 x^7}{625}-\frac {4 x^3 \log ^3(x)}{1875}+\frac {1}{625} x^3 \log ^4(x)+\frac {1}{625} \int \left (64 x^2 \log ^3(x)+64 x^3 \log ^3(x)\right ) \, dx+\frac {4}{625} \int x^2 \log ^2(x) \, dx+\frac {4}{25} \int x \log ^2(x) \, dx+\frac {96}{125} \int x^4 \log ^2(x) \, dx+\frac {102}{125} \int x^2 \log ^2(x) \, dx+\frac {1008}{625} \int x^3 \log ^2(x) \, dx+\frac {44}{25} \int x \log (x) \, dx+\frac {1536}{625} \int x^5 \log (x) \, dx+\frac {24}{5} \int x^2 \log (x) \, dx+\frac {4992}{625} \int x^4 \log (x) \, dx+\frac {1056}{125} \int x^3 \log (x) \, dx\\ &=x+\frac {49 x^2}{25}+\frac {311 x^3}{75}+\frac {554 x^4}{125}+\frac {59808 x^5}{15625}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {22}{25} x^2 \log (x)+\frac {8}{5} x^3 \log (x)+\frac {264}{125} x^4 \log (x)+\frac {4992 x^5 \log (x)}{3125}+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {514 x^3 \log ^2(x)}{1875}+\frac {252}{625} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)-\frac {4 x^3 \log ^3(x)}{1875}+\frac {1}{625} x^3 \log ^4(x)-\frac {8 \int x^2 \log (x) \, dx}{1875}+\frac {64}{625} \int x^2 \log ^3(x) \, dx+\frac {64}{625} \int x^3 \log ^3(x) \, dx-\frac {4}{25} \int x \log (x) \, dx-\frac {192}{625} \int x^4 \log (x) \, dx-\frac {68}{125} \int x^2 \log (x) \, dx-\frac {504}{625} \int x^3 \log (x) \, dx\\ &=x+2 x^2+\frac {71003 x^3}{16875}+\frac {5603 x^4}{1250}+\frac {96 x^5}{25}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {4}{5} x^2 \log (x)+\frac {7972 x^3 \log (x)}{5625}+\frac {1194}{625} x^4 \log (x)+\frac {192}{125} x^5 \log (x)+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {514 x^3 \log ^2(x)}{1875}+\frac {252}{625} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {16}{625} x^4 \log ^3(x)+\frac {1}{625} x^3 \log ^4(x)-\frac {48}{625} \int x^3 \log ^2(x) \, dx-\frac {64}{625} \int x^2 \log ^2(x) \, dx\\ &=x+2 x^2+\frac {71003 x^3}{16875}+\frac {5603 x^4}{1250}+\frac {96 x^5}{25}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {4}{5} x^2 \log (x)+\frac {7972 x^3 \log (x)}{5625}+\frac {1194}{625} x^4 \log (x)+\frac {192}{125} x^5 \log (x)+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {6}{25} x^3 \log ^2(x)+\frac {48}{125} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {16}{625} x^4 \log ^3(x)+\frac {1}{625} x^3 \log ^4(x)+\frac {24}{625} \int x^3 \log (x) \, dx+\frac {128 \int x^2 \log (x) \, dx}{1875}\\ &=x+2 x^2+\frac {21 x^3}{5}+\frac {112 x^4}{25}+\frac {96 x^5}{25}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {4}{5} x^2 \log (x)+\frac {36}{25} x^3 \log (x)+\frac {48}{25} x^4 \log (x)+\frac {192}{125} x^5 \log (x)+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {6}{25} x^3 \log ^2(x)+\frac {48}{125} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {16}{625} x^4 \log ^3(x)+\frac {1}{625} x^3 \log ^4(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.02, size = 164, normalized size = 7.13 \begin {gather*} x+2 x^2+\frac {21 x^3}{5}+\frac {112 x^4}{25}+\frac {96 x^5}{25}+\frac {256 x^6}{125}+\frac {256 x^7}{625}+\frac {4}{5} x^2 \log (x)+\frac {36}{25} x^3 \log (x)+\frac {48}{25} x^4 \log (x)+\frac {192}{125} x^5 \log (x)+\frac {256}{625} x^6 \log (x)+\frac {2}{25} x^2 \log ^2(x)+\frac {6}{25} x^3 \log ^2(x)+\frac {48}{125} x^4 \log ^2(x)+\frac {96}{625} x^5 \log ^2(x)+\frac {4}{125} x^3 \log ^3(x)+\frac {16}{625} x^4 \log ^3(x)+\frac {1}{625} x^3 \log ^4(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(625 + 3000*x + 8775*x^2 + 12400*x^3 + 12960*x^4 + 7936*x^5 + 1792*x^6 + (1100*x + 3000*x^2 + 5280*x
^3 + 4992*x^4 + 1536*x^5)*Log[x] + (100*x + 510*x^2 + 1008*x^3 + 480*x^4)*Log[x]^2 + (64*x^2 + 64*x^3)*Log[x]^
3 + 3*x^2*Log[x]^4)/625,x]

[Out]

x + 2*x^2 + (21*x^3)/5 + (112*x^4)/25 + (96*x^5)/25 + (256*x^6)/125 + (256*x^7)/625 + (4*x^2*Log[x])/5 + (36*x
^3*Log[x])/25 + (48*x^4*Log[x])/25 + (192*x^5*Log[x])/125 + (256*x^6*Log[x])/625 + (2*x^2*Log[x]^2)/25 + (6*x^
3*Log[x]^2)/25 + (48*x^4*Log[x]^2)/125 + (96*x^5*Log[x]^2)/625 + (4*x^3*Log[x]^3)/125 + (16*x^4*Log[x]^3)/625
+ (x^3*Log[x]^4)/625

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fricas [B]  time = 0.75, size = 115, normalized size = 5.00 \begin {gather*} \frac {256}{625} \, x^{7} + \frac {1}{625} \, x^{3} \log \relax (x)^{4} + \frac {256}{125} \, x^{6} + \frac {96}{25} \, x^{5} + \frac {112}{25} \, x^{4} + \frac {4}{625} \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (x)^{3} + \frac {21}{5} \, x^{3} + \frac {2}{625} \, {\left (48 \, x^{5} + 120 \, x^{4} + 75 \, x^{3} + 25 \, x^{2}\right )} \log \relax (x)^{2} + 2 \, x^{2} + \frac {4}{625} \, {\left (64 \, x^{6} + 240 \, x^{5} + 300 \, x^{4} + 225 \, x^{3} + 125 \, x^{2}\right )} \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4+1008*x^3+510*x^2+100*x)*log(x)^2+1/
625*(1536*x^5+4992*x^4+5280*x^3+3000*x^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/
25*x^2+24/5*x+1,x, algorithm="fricas")

[Out]

256/625*x^7 + 1/625*x^3*log(x)^4 + 256/125*x^6 + 96/25*x^5 + 112/25*x^4 + 4/625*(4*x^4 + 5*x^3)*log(x)^3 + 21/
5*x^3 + 2/625*(48*x^5 + 120*x^4 + 75*x^3 + 25*x^2)*log(x)^2 + 2*x^2 + 4/625*(64*x^6 + 240*x^5 + 300*x^4 + 225*
x^3 + 125*x^2)*log(x) + x

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giac [B]  time = 0.19, size = 130, normalized size = 5.65 \begin {gather*} \frac {256}{625} \, x^{7} + \frac {256}{625} \, x^{6} \log \relax (x) + \frac {96}{625} \, x^{5} \log \relax (x)^{2} + \frac {16}{625} \, x^{4} \log \relax (x)^{3} + \frac {1}{625} \, x^{3} \log \relax (x)^{4} + \frac {256}{125} \, x^{6} + \frac {192}{125} \, x^{5} \log \relax (x) + \frac {48}{125} \, x^{4} \log \relax (x)^{2} + \frac {4}{125} \, x^{3} \log \relax (x)^{3} + \frac {96}{25} \, x^{5} + \frac {48}{25} \, x^{4} \log \relax (x) + \frac {6}{25} \, x^{3} \log \relax (x)^{2} + \frac {112}{25} \, x^{4} + \frac {36}{25} \, x^{3} \log \relax (x) + \frac {2}{25} \, x^{2} \log \relax (x)^{2} + \frac {21}{5} \, x^{3} + \frac {4}{5} \, x^{2} \log \relax (x) + 2 \, x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4+1008*x^3+510*x^2+100*x)*log(x)^2+1/
625*(1536*x^5+4992*x^4+5280*x^3+3000*x^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/
25*x^2+24/5*x+1,x, algorithm="giac")

[Out]

256/625*x^7 + 256/625*x^6*log(x) + 96/625*x^5*log(x)^2 + 16/625*x^4*log(x)^3 + 1/625*x^3*log(x)^4 + 256/125*x^
6 + 192/125*x^5*log(x) + 48/125*x^4*log(x)^2 + 4/125*x^3*log(x)^3 + 96/25*x^5 + 48/25*x^4*log(x) + 6/25*x^3*lo
g(x)^2 + 112/25*x^4 + 36/25*x^3*log(x) + 2/25*x^2*log(x)^2 + 21/5*x^3 + 4/5*x^2*log(x) + 2*x^2 + x

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maple [B]  time = 0.03, size = 131, normalized size = 5.70

method	result	size
default	\(x +\frac {4 x^{2} \ln \relax (x )}{5}+\frac {2 x^{2} \ln \relax (x )^{2}}{25}+\frac {256 x^{7}}{625}+\frac {256 x^{6}}{125}+\frac {96 x^{5}}{25}+\frac {112 x^{4}}{25}+\frac {21 x^{3}}{5}+2 x^{2}+\frac {36 x^{3} \ln \relax (x )}{25}+\frac {256 x^{6} \ln \relax (x )}{625}+\frac {16 x^{4} \ln \relax (x )^{3}}{625}+\frac {4 x^{3} \ln \relax (x )^{3}}{125}+\frac {192 x^{5} \ln \relax (x )}{125}+\frac {x^{3} \ln \relax (x )^{4}}{625}+\frac {48 x^{4} \ln \relax (x )^{2}}{125}+\frac {48 x^{4} \ln \relax (x )}{25}+\frac {96 x^{5} \ln \relax (x )^{2}}{625}+\frac {6 x^{3} \ln \relax (x )^{2}}{25}\)	\(131\)
risch	\(x +\frac {4 x^{2} \ln \relax (x )}{5}+\frac {2 x^{2} \ln \relax (x )^{2}}{25}+\frac {256 x^{7}}{625}+\frac {256 x^{6}}{125}+\frac {96 x^{5}}{25}+\frac {112 x^{4}}{25}+\frac {21 x^{3}}{5}+2 x^{2}+\frac {36 x^{3} \ln \relax (x )}{25}+\frac {256 x^{6} \ln \relax (x )}{625}+\frac {16 x^{4} \ln \relax (x )^{3}}{625}+\frac {4 x^{3} \ln \relax (x )^{3}}{125}+\frac {192 x^{5} \ln \relax (x )}{125}+\frac {x^{3} \ln \relax (x )^{4}}{625}+\frac {48 x^{4} \ln \relax (x )^{2}}{125}+\frac {48 x^{4} \ln \relax (x )}{25}+\frac {96 x^{5} \ln \relax (x )^{2}}{625}+\frac {6 x^{3} \ln \relax (x )^{2}}{25}\)	\(131\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3/625*x^2*ln(x)^4+1/625*(64*x^3+64*x^2)*ln(x)^3+1/625*(480*x^4+1008*x^3+510*x^2+100*x)*ln(x)^2+1/625*(1536
*x^5+4992*x^4+5280*x^3+3000*x^2+1100*x)*ln(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/25*x^2+24/
5*x+1,x,method=_RETURNVERBOSE)

[Out]

x+4/5*x^2*ln(x)+2/25*x^2*ln(x)^2+256/625*x^7+256/125*x^6+96/25*x^5+112/25*x^4+21/5*x^3+2*x^2+36/25*x^3*ln(x)+2
56/625*x^6*ln(x)+16/625*x^4*ln(x)^3+4/125*x^3*ln(x)^3+192/125*x^5*ln(x)+1/625*x^3*ln(x)^4+48/125*x^4*ln(x)^2+4
8/25*x^4*ln(x)+96/625*x^5*ln(x)^2+6/25*x^3*ln(x)^2

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maxima [B]  time = 0.37, size = 205, normalized size = 8.91 \begin {gather*} \frac {256}{625} \, x^{7} + \frac {96}{15625} \, {\left (25 \, \log \relax (x)^{2} - 10 \, \log \relax (x) + 2\right )} x^{5} + \frac {256}{125} \, x^{6} + \frac {1}{1250} \, {\left (32 \, \log \relax (x)^{3} - 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) - 3\right )} x^{4} + \frac {63}{1250} \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} + \frac {59808}{15625} \, x^{5} + \frac {1}{16875} \, {\left (27 \, \log \relax (x)^{4} - 36 \, \log \relax (x)^{3} + 36 \, \log \relax (x)^{2} - 24 \, \log \relax (x) + 8\right )} x^{3} + \frac {64}{16875} \, {\left (9 \, \log \relax (x)^{3} - 9 \, \log \relax (x)^{2} + 6 \, \log \relax (x) - 2\right )} x^{3} + \frac {34}{1125} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} + \frac {554}{125} \, x^{4} + \frac {1}{25} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + \frac {311}{75} \, x^{3} + \frac {49}{25} \, x^{2} + \frac {2}{3125} \, {\left (640 \, x^{6} + 2496 \, x^{5} + 3300 \, x^{4} + 2500 \, x^{3} + 1375 \, x^{2}\right )} \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/625*x^2*log(x)^4+1/625*(64*x^3+64*x^2)*log(x)^3+1/625*(480*x^4+1008*x^3+510*x^2+100*x)*log(x)^2+1/
625*(1536*x^5+4992*x^4+5280*x^3+3000*x^2+1100*x)*log(x)+1792/625*x^6+7936/625*x^5+2592/125*x^4+496/25*x^3+351/
25*x^2+24/5*x+1,x, algorithm="maxima")

[Out]

256/625*x^7 + 96/15625*(25*log(x)^2 - 10*log(x) + 2)*x^5 + 256/125*x^6 + 1/1250*(32*log(x)^3 - 24*log(x)^2 + 1
2*log(x) - 3)*x^4 + 63/1250*(8*log(x)^2 - 4*log(x) + 1)*x^4 + 59808/15625*x^5 + 1/16875*(27*log(x)^4 - 36*log(
x)^3 + 36*log(x)^2 - 24*log(x) + 8)*x^3 + 64/16875*(9*log(x)^3 - 9*log(x)^2 + 6*log(x) - 2)*x^3 + 34/1125*(9*l
og(x)^2 - 6*log(x) + 2)*x^3 + 554/125*x^4 + 1/25*(2*log(x)^2 - 2*log(x) + 1)*x^2 + 311/75*x^3 + 49/25*x^2 + 2/
3125*(640*x^6 + 2496*x^5 + 3300*x^4 + 2500*x^3 + 1375*x^2)*log(x) + x

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mupad [B]  time = 2.53, size = 38, normalized size = 1.65 \begin {gather*} \frac {x\,{\left (16\,x^3+8\,x^2\,\ln \relax (x)+40\,x^2+x\,{\ln \relax (x)}^2+10\,x\,\ln \relax (x)+25\,x+25\right )}^2}{625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x)/5 + (log(x)*(1100*x + 3000*x^2 + 5280*x^3 + 4992*x^4 + 1536*x^5))/625 + (log(x)^3*(64*x^2 + 64*x^3)
)/625 + (3*x^2*log(x)^4)/625 + (log(x)^2*(100*x + 510*x^2 + 1008*x^3 + 480*x^4))/625 + (351*x^2)/25 + (496*x^3
)/25 + (2592*x^4)/125 + (7936*x^5)/625 + (1792*x^6)/625 + 1,x)

[Out]

(x*(25*x + x*log(x)^2 + 8*x^2*log(x) + 10*x*log(x) + 40*x^2 + 16*x^3 + 25)^2)/625

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sympy [B]  time = 0.27, size = 138, normalized size = 6.00 \begin {gather*} \frac {256 x^{7}}{625} + \frac {256 x^{6}}{125} + \frac {96 x^{5}}{25} + \frac {112 x^{4}}{25} + \frac {x^{3} \log {\relax (x )}^{4}}{625} + \frac {21 x^{3}}{5} + 2 x^{2} + x + \left (\frac {16 x^{4}}{625} + \frac {4 x^{3}}{125}\right ) \log {\relax (x )}^{3} + \left (\frac {96 x^{5}}{625} + \frac {48 x^{4}}{125} + \frac {6 x^{3}}{25} + \frac {2 x^{2}}{25}\right ) \log {\relax (x )}^{2} + \left (\frac {256 x^{6}}{625} + \frac {192 x^{5}}{125} + \frac {48 x^{4}}{25} + \frac {36 x^{3}}{25} + \frac {4 x^{2}}{5}\right ) \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/625*x**2*ln(x)**4+1/625*(64*x**3+64*x**2)*ln(x)**3+1/625*(480*x**4+1008*x**3+510*x**2+100*x)*ln(x)
**2+1/625*(1536*x**5+4992*x**4+5280*x**3+3000*x**2+1100*x)*ln(x)+1792/625*x**6+7936/625*x**5+2592/125*x**4+496
/25*x**3+351/25*x**2+24/5*x+1,x)

[Out]

256*x**7/625 + 256*x**6/125 + 96*x**5/25 + 112*x**4/25 + x**3*log(x)**4/625 + 21*x**3/5 + 2*x**2 + x + (16*x**
4/625 + 4*x**3/125)*log(x)**3 + (96*x**5/625 + 48*x**4/125 + 6*x**3/25 + 2*x**2/25)*log(x)**2 + (256*x**6/625
+ 192*x**5/125 + 48*x**4/25 + 36*x**3/25 + 4*x**2/5)*log(x)

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