3.88.35 \(\int \frac {1100 x+1080 x^2+332 x^3+32 x^4+(1000+1040 x+328 x^2+32 x^3) \log (5)+(6000 x+10000 x^2+5760 x^3+1408 x^4+128 x^5+(5000+9000 x+5440 x^2+1376 x^3+128 x^4) \log (5)) \log (x)+(2500 x+8000 x^2+7200 x^3+2560 x^4+320 x^5+(4000 x+4800 x^2+1920 x^3+256 x^4) \log (5)) \log ^2(x)}{x} \, dx\)

Optimal. Leaf size=21 \[ 4 (x+\log (5)) \left (5+x+(-5-2 x)^2 \log (x)\right )^2 \]

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Rubi [B]  time = 0.44, antiderivative size = 294, normalized size of antiderivative = 14.00, number of steps used = 24, number of rules used = 9, integrand size = 142, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.063, Rules used = {14, 1620, 2357, 2304, 2301, 2295, 2356, 2305, 2296} \begin {gather*} 64 x^5 \log ^2(x)+8 x^4+64 x^4 (10+\log (5)) \log ^2(x)+16 x^4 (22+\log (25)) \log (x)-32 x^4 (10+\log (5)) \log (x)-4 x^4 (22+\log (25))+8 x^4 (10+\log (5))+160 x^3 (15+\log (625)) \log ^2(x)-\frac {320}{3} x^3 (15+\log (625)) \log (x)+\frac {32}{3} x^3 (180+33 \log (5)+5 \log (25)) \log (x)+\frac {320}{9} x^3 (15+\log (625))-\frac {32}{9} x^3 (180+33 \log (5)+5 \log (25))+\frac {4}{3} x^3 (83+8 \log (5))+800 x^2 (5+\log (125)) \log ^2(x)-800 x^2 (5+\log (125)) \log (x)+40 x^2 (125+68 \log (5)) \log (x)+400 x^2 (5+\log (125))-20 x^2 (125+68 \log (5))+4 x^2 (135+41 \log (5))+500 x (5+8 \log (5)) \log ^2(x)+2500 \log (5) \log ^2(x)+3000 x (2+\log (125)) \log (x)-1000 x (5+8 \log (5)) \log (x)-3000 x (2+\log (125))+20 x (55+52 \log (5))+1000 x (5+8 \log (5))+1000 \log (5) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1100*x + 1080*x^2 + 332*x^3 + 32*x^4 + (1000 + 1040*x + 328*x^2 + 32*x^3)*Log[5] + (6000*x + 10000*x^2 +
5760*x^3 + 1408*x^4 + 128*x^5 + (5000 + 9000*x + 5440*x^2 + 1376*x^3 + 128*x^4)*Log[5])*Log[x] + (2500*x + 800
0*x^2 + 7200*x^3 + 2560*x^4 + 320*x^5 + (4000*x + 4800*x^2 + 1920*x^3 + 256*x^4)*Log[5])*Log[x]^2)/x,x]

[Out]

8*x^4 + 8*x^4*(10 + Log[5]) + 1000*x*(5 + 8*Log[5]) + (4*x^3*(83 + 8*Log[5]))/3 + 4*x^2*(135 + 41*Log[5]) + 20
*x*(55 + 52*Log[5]) - 20*x^2*(125 + 68*Log[5]) - 4*x^4*(22 + Log[25]) - (32*x^3*(180 + 33*Log[5] + 5*Log[25]))
/9 - 3000*x*(2 + Log[125]) + 400*x^2*(5 + Log[125]) + (320*x^3*(15 + Log[625]))/9 + 1000*Log[5]*Log[x] - 32*x^
4*(10 + Log[5])*Log[x] - 1000*x*(5 + 8*Log[5])*Log[x] + 40*x^2*(125 + 68*Log[5])*Log[x] + 16*x^4*(22 + Log[25]
)*Log[x] + (32*x^3*(180 + 33*Log[5] + 5*Log[25])*Log[x])/3 + 3000*x*(2 + Log[125])*Log[x] - 800*x^2*(5 + Log[1
25])*Log[x] - (320*x^3*(15 + Log[625])*Log[x])/3 + 64*x^5*Log[x]^2 + 2500*Log[5]*Log[x]^2 + 64*x^4*(10 + Log[5
])*Log[x]^2 + 500*x*(5 + 8*Log[5])*Log[x]^2 + 800*x^2*(5 + Log[125])*Log[x]^2 + 160*x^3*(15 + Log[625])*Log[x]
^2

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 1620

Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)
^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2]) &&
GtQ[Expon[Px, x], 2]

Rule 2295

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

Rule 2296

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 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

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 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]

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]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4 (5+x) \left (8 x^3+50 \log (5)+x^2 (43+8 \log (5))+x (55+42 \log (5))\right )}{x}+\frac {8 (5+2 x) \left (8 x^4+125 \log (5)+25 x (6+7 \log (5))+2 x^2 (95+33 \log (5))+4 x^3 (17+\log (25))\right ) \log (x)}{x}+4 (5+2 x)^3 (5+10 x+8 \log (5)) \log ^2(x)\right ) \, dx\\ &=4 \int \frac {(5+x) \left (8 x^3+50 \log (5)+x^2 (43+8 \log (5))+x (55+42 \log (5))\right )}{x} \, dx+4 \int (5+2 x)^3 (5+10 x+8 \log (5)) \log ^2(x) \, dx+8 \int \frac {(5+2 x) \left (8 x^4+125 \log (5)+25 x (6+7 \log (5))+2 x^2 (95+33 \log (5))+4 x^3 (17+\log (25))\right ) \log (x)}{x} \, dx\\ &=4 \int \left (8 x^3+\frac {250 \log (5)}{x}+x^2 (83+8 \log (5))+2 x (135+41 \log (5))+5 (55+52 \log (5))\right ) \, dx+4 \int \left (80 x^4 \log ^2(x)+64 x^3 (10+\log (5)) \log ^2(x)+125 (5+8 \log (5)) \log ^2(x)+400 x (5+\log (125)) \log ^2(x)+120 x^2 (15+\log (625)) \log ^2(x)\right ) \, dx+8 \int \left (16 x^4 \log (x)+\frac {625 \log (5) \log (x)}{x}+10 x (125+68 \log (5)) \log (x)+8 x^3 (22+\log (25)) \log (x)+4 x^2 (180+33 \log (5)+5 \log (25)) \log (x)+375 (2+\log (125)) \log (x)\right ) \, dx\\ &=8 x^4+\frac {4}{3} x^3 (83+8 \log (5))+4 x^2 (135+41 \log (5))+20 x (55+52 \log (5))+1000 \log (5) \log (x)+128 \int x^4 \log (x) \, dx+320 \int x^4 \log ^2(x) \, dx+(5000 \log (5)) \int \frac {\log (x)}{x} \, dx+(256 (10+\log (5))) \int x^3 \log ^2(x) \, dx+(500 (5+8 \log (5))) \int \log ^2(x) \, dx+(80 (125+68 \log (5))) \int x \log (x) \, dx+(64 (22+\log (25))) \int x^3 \log (x) \, dx+(32 (180+33 \log (5)+5 \log (25))) \int x^2 \log (x) \, dx+(3000 (2+\log (125))) \int \log (x) \, dx+(1600 (5+\log (125))) \int x \log ^2(x) \, dx+(480 (15+\log (625))) \int x^2 \log ^2(x) \, dx\\ &=8 x^4-\frac {128 x^5}{25}+\frac {4}{3} x^3 (83+8 \log (5))+4 x^2 (135+41 \log (5))+20 x (55+52 \log (5))-20 x^2 (125+68 \log (5))-4 x^4 (22+\log (25))-\frac {32}{9} x^3 (180+33 \log (5)+5 \log (25))-3000 x (2+\log (125))+\frac {128}{5} x^5 \log (x)+1000 \log (5) \log (x)+40 x^2 (125+68 \log (5)) \log (x)+16 x^4 (22+\log (25)) \log (x)+\frac {32}{3} x^3 (180+33 \log (5)+5 \log (25)) \log (x)+3000 x (2+\log (125)) \log (x)+64 x^5 \log ^2(x)+2500 \log (5) \log ^2(x)+64 x^4 (10+\log (5)) \log ^2(x)+500 x (5+8 \log (5)) \log ^2(x)+800 x^2 (5+\log (125)) \log ^2(x)+160 x^3 (15+\log (625)) \log ^2(x)-128 \int x^4 \log (x) \, dx-(128 (10+\log (5))) \int x^3 \log (x) \, dx-(1000 (5+8 \log (5))) \int \log (x) \, dx-(1600 (5+\log (125))) \int x \log (x) \, dx-(320 (15+\log (625))) \int x^2 \log (x) \, dx\\ &=8 x^4+8 x^4 (10+\log (5))+1000 x (5+8 \log (5))+\frac {4}{3} x^3 (83+8 \log (5))+4 x^2 (135+41 \log (5))+20 x (55+52 \log (5))-20 x^2 (125+68 \log (5))-4 x^4 (22+\log (25))-\frac {32}{9} x^3 (180+33 \log (5)+5 \log (25))-3000 x (2+\log (125))+400 x^2 (5+\log (125))+\frac {320}{9} x^3 (15+\log (625))+1000 \log (5) \log (x)-32 x^4 (10+\log (5)) \log (x)-1000 x (5+8 \log (5)) \log (x)+40 x^2 (125+68 \log (5)) \log (x)+16 x^4 (22+\log (25)) \log (x)+\frac {32}{3} x^3 (180+33 \log (5)+5 \log (25)) \log (x)+3000 x (2+\log (125)) \log (x)-800 x^2 (5+\log (125)) \log (x)-\frac {320}{3} x^3 (15+\log (625)) \log (x)+64 x^5 \log ^2(x)+2500 \log (5) \log ^2(x)+64 x^4 (10+\log (5)) \log ^2(x)+500 x (5+8 \log (5)) \log ^2(x)+800 x^2 (5+\log (125)) \log ^2(x)+160 x^3 (15+\log (625)) \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.29, size = 235, normalized size = 11.19 \begin {gather*} 4 \left (25 x+10 x^2+x^3+2260 x \log (5)-299 x^2 \log (5)-\frac {320}{9} x^3 \log (5)-750 x \log (125)+100 x^2 \log (125)+\frac {80}{9} x^3 \log (625)+250 x \log (x)+250 x^2 \log (x)+80 x^3 \log (x)+8 x^4 \log (x)+250 \log (5) \log (x)-2000 x \log (5) \log (x)+680 x^2 \log (5) \log (x)+\frac {344}{3} x^3 \log (5) \log (x)+750 x \log (125) \log (x)-200 x^2 \log (125) \log (x)-\frac {80}{3} x^3 \log (625) \log (x)+625 x \log ^2(x)+1000 x^2 \log ^2(x)+600 x^3 \log ^2(x)+160 x^4 \log ^2(x)+16 x^5 \log ^2(x)+625 \log (5) \log ^2(x)+1000 x \log (5) \log ^2(x)+16 x^4 \log (5) \log ^2(x)+200 x^2 \log (125) \log ^2(x)+40 x^3 \log (625) \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1100*x + 1080*x^2 + 332*x^3 + 32*x^4 + (1000 + 1040*x + 328*x^2 + 32*x^3)*Log[5] + (6000*x + 10000*
x^2 + 5760*x^3 + 1408*x^4 + 128*x^5 + (5000 + 9000*x + 5440*x^2 + 1376*x^3 + 128*x^4)*Log[5])*Log[x] + (2500*x
+ 8000*x^2 + 7200*x^3 + 2560*x^4 + 320*x^5 + (4000*x + 4800*x^2 + 1920*x^3 + 256*x^4)*Log[5])*Log[x]^2)/x,x]

[Out]

4*(25*x + 10*x^2 + x^3 + 2260*x*Log[5] - 299*x^2*Log[5] - (320*x^3*Log[5])/9 - 750*x*Log[125] + 100*x^2*Log[12
5] + (80*x^3*Log[625])/9 + 250*x*Log[x] + 250*x^2*Log[x] + 80*x^3*Log[x] + 8*x^4*Log[x] + 250*Log[5]*Log[x] -
2000*x*Log[5]*Log[x] + 680*x^2*Log[5]*Log[x] + (344*x^3*Log[5]*Log[x])/3 + 750*x*Log[125]*Log[x] - 200*x^2*Log
[125]*Log[x] - (80*x^3*Log[625]*Log[x])/3 + 625*x*Log[x]^2 + 1000*x^2*Log[x]^2 + 600*x^3*Log[x]^2 + 160*x^4*Lo
g[x]^2 + 16*x^5*Log[x]^2 + 625*Log[5]*Log[x]^2 + 1000*x*Log[5]*Log[x]^2 + 16*x^4*Log[5]*Log[x]^2 + 200*x^2*Log
[125]*Log[x]^2 + 40*x^3*Log[625]*Log[x]^2)

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fricas [B]  time = 0.77, size = 119, normalized size = 5.67 \begin {gather*} 4 \, x^{3} + 4 \, {\left (16 \, x^{5} + 160 \, x^{4} + 600 \, x^{3} + 1000 \, x^{2} + {\left (16 \, x^{4} + 160 \, x^{3} + 600 \, x^{2} + 1000 \, x + 625\right )} \log \relax (5) + 625 \, x\right )} \log \relax (x)^{2} + 40 \, x^{2} + 4 \, {\left (x^{2} + 10 \, x\right )} \log \relax (5) + 8 \, {\left (4 \, x^{4} + 40 \, x^{3} + 125 \, x^{2} + {\left (4 \, x^{3} + 40 \, x^{2} + 125 \, x + 125\right )} \log \relax (5) + 125 \, x\right )} \log \relax (x) + 100 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^4+1920*x^3+4800*x^2+4000*x)*log(5)+320*x^5+2560*x^4+7200*x^3+8000*x^2+2500*x)*log(x)^2+((12
8*x^4+1376*x^3+5440*x^2+9000*x+5000)*log(5)+128*x^5+1408*x^4+5760*x^3+10000*x^2+6000*x)*log(x)+(32*x^3+328*x^2
+1040*x+1000)*log(5)+32*x^4+332*x^3+1080*x^2+1100*x)/x,x, algorithm="fricas")

[Out]

4*x^3 + 4*(16*x^5 + 160*x^4 + 600*x^3 + 1000*x^2 + (16*x^4 + 160*x^3 + 600*x^2 + 1000*x + 625)*log(5) + 625*x)
*log(x)^2 + 40*x^2 + 4*(x^2 + 10*x)*log(5) + 8*(4*x^4 + 40*x^3 + 125*x^2 + (4*x^3 + 40*x^2 + 125*x + 125)*log(
5) + 125*x)*log(x) + 100*x

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giac [B]  time = 0.23, size = 123, normalized size = 5.86 \begin {gather*} 4 \, x^{3} + 4 \, x^{2} {\left (\log \relax (5) + 10\right )} + 4 \, {\left (16 \, x^{5} + 16 \, x^{4} {\left (\log \relax (5) + 10\right )} + 40 \, x^{3} {\left (4 \, \log \relax (5) + 15\right )} + 200 \, x^{2} {\left (3 \, \log \relax (5) + 5\right )} + 125 \, x {\left (8 \, \log \relax (5) + 5\right )} + 625 \, \log \relax (5)\right )} \log \relax (x)^{2} + 20 \, x {\left (2 \, \log \relax (5) + 5\right )} + 8 \, {\left (4 \, x^{4} + 4 \, x^{3} {\left (\log \relax (5) + 10\right )} + 5 \, x^{2} {\left (8 \, \log \relax (5) + 25\right )} + 125 \, x {\left (\log \relax (5) + 1\right )}\right )} \log \relax (x) + 1000 \, \log \relax (5) \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^4+1920*x^3+4800*x^2+4000*x)*log(5)+320*x^5+2560*x^4+7200*x^3+8000*x^2+2500*x)*log(x)^2+((12
8*x^4+1376*x^3+5440*x^2+9000*x+5000)*log(5)+128*x^5+1408*x^4+5760*x^3+10000*x^2+6000*x)*log(x)+(32*x^3+328*x^2
+1040*x+1000)*log(5)+32*x^4+332*x^3+1080*x^2+1100*x)/x,x, algorithm="giac")

[Out]

4*x^3 + 4*x^2*(log(5) + 10) + 4*(16*x^5 + 16*x^4*(log(5) + 10) + 40*x^3*(4*log(5) + 15) + 200*x^2*(3*log(5) +
5) + 125*x*(8*log(5) + 5) + 625*log(5))*log(x)^2 + 20*x*(2*log(5) + 5) + 8*(4*x^4 + 4*x^3*(log(5) + 10) + 5*x^
2*(8*log(5) + 25) + 125*x*(log(5) + 1))*log(x) + 1000*log(5)*log(x)

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maple [B]  time = 0.07, size = 133, normalized size = 6.33

method	result	size
risch	\(\left (64 x^{4} \ln \relax (5)+64 x^{5}+640 x^{3} \ln \relax (5)+640 x^{4}+2400 x^{2} \ln \relax (5)+2400 x^{3}+4000 x \ln \relax (5)+4000 x^{2}+2500 \ln \relax (5)+2500 x \right ) \ln \relax (x )^{2}+\left (32 x^{3} \ln \relax (5)+32 x^{4}+320 x^{2} \ln \relax (5)+320 x^{3}+1000 x \ln \relax (5)+1000 x^{2}+1000 x \right ) \ln \relax (x )+4 x^{2} \ln \relax (5)+4 x^{3}+40 x \ln \relax (5)+40 x^{2}+100 x +1000 \ln \relax (5) \ln \relax (x )\)	\(133\)
norman	\(\left (40+4 \ln \relax (5)\right ) x^{2}+\left (100+40 \ln \relax (5)\right ) x +1000 \ln \relax (5) \ln \relax (x )+\left (320+32 \ln \relax (5)\right ) x^{3} \ln \relax (x )+\left (640+64 \ln \relax (5)\right ) x^{4} \ln \relax (x )^{2}+\left (1000+320 \ln \relax (5)\right ) x^{2} \ln \relax (x )+\left (1000+1000 \ln \relax (5)\right ) x \ln \relax (x )+\left (2400+640 \ln \relax (5)\right ) x^{3} \ln \relax (x )^{2}+\left (2500+4000 \ln \relax (5)\right ) x \ln \relax (x )^{2}+\left (4000+2400 \ln \relax (5)\right ) x^{2} \ln \relax (x )^{2}+4 x^{3}+32 x^{4} \ln \relax (x )+64 x^{5} \ln \relax (x )^{2}+2500 \ln \relax (5) \ln \relax (x )^{2}\)	\(143\)
default	\(100 x +1000 x^{2} \ln \relax (x )+164 x^{2} \ln \relax (5)+4000 x^{2} \ln \relax (x )^{2}+4 x^{3}+40 x^{2}+320 x^{3} \ln \relax (x )+640 x^{4} \ln \relax (x )^{2}+1040 x \ln \relax (5)+32 x^{4} \ln \relax (x )+2500 x \ln \relax (x )^{2}+\frac {32 x^{3} \ln \relax (5)}{3}+1000 x \ln \relax (x )+64 x^{5} \ln \relax (x )^{2}+1000 \ln \relax (5) \ln \relax (x )+2400 x^{3} \ln \relax (x )^{2}+4000 \ln \relax (5) \left (x \ln \relax (x )^{2}-2 x \ln \relax (x )+2 x \right )+4800 \ln \relax (5) \left (\frac {x^{2} \ln \relax (x )^{2}}{2}-\frac {x^{2} \ln \relax (x )}{2}+\frac {x^{2}}{4}\right )+256 \ln \relax (5) \left (\frac {x^{4} \ln \relax (x )^{2}}{4}-\frac {x^{4} \ln \relax (x )}{8}+\frac {x^{4}}{32}\right )+128 \ln \relax (5) \left (\frac {x^{4} \ln \relax (x )}{4}-\frac {x^{4}}{16}\right )+1920 \ln \relax (5) \left (\frac {x^{3} \ln \relax (x )^{2}}{3}-\frac {2 x^{3} \ln \relax (x )}{9}+\frac {2 x^{3}}{27}\right )+1376 \ln \relax (5) \left (\frac {x^{3} \ln \relax (x )}{3}-\frac {x^{3}}{9}\right )+9000 \ln \relax (5) \left (x \ln \relax (x )-x \right )+5440 \ln \relax (5) \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )+2500 \ln \relax (5) \ln \relax (x )^{2}\)	\(277\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((256*x^4+1920*x^3+4800*x^2+4000*x)*ln(5)+320*x^5+2560*x^4+7200*x^3+8000*x^2+2500*x)*ln(x)^2+((128*x^4+13
76*x^3+5440*x^2+9000*x+5000)*ln(5)+128*x^5+1408*x^4+5760*x^3+10000*x^2+6000*x)*ln(x)+(32*x^3+328*x^2+1040*x+10
00)*ln(5)+32*x^4+332*x^3+1080*x^2+1100*x)/x,x,method=_RETURNVERBOSE)

[Out]

(64*x^4*ln(5)+64*x^5+640*x^3*ln(5)+640*x^4+2400*x^2*ln(5)+2400*x^3+4000*x*ln(5)+4000*x^2+2500*ln(5)+2500*x)*ln
(x)^2+(32*x^3*ln(5)+32*x^4+320*x^2*ln(5)+320*x^3+1000*x*ln(5)+1000*x^2+1000*x)*ln(x)+4*x^2*ln(5)+4*x^3+40*x*ln
(5)+40*x^2+100*x+1000*ln(5)*ln(x)

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maxima [B]  time = 0.36, size = 306, normalized size = 14.57 \begin {gather*} \frac {64}{25} \, {\left (25 \, \log \relax (x)^{2} - 10 \, \log \relax (x) + 2\right )} x^{5} + 8 \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} \log \relax (5) + \frac {128}{5} \, x^{5} \log \relax (x) + 80 \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} - \frac {128}{25} \, x^{5} + \frac {640}{9} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} \log \relax (5) + 352 \, x^{4} \log \relax (x) + \frac {800}{3} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} - 80 \, x^{4} + 1200 \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} \log \relax (5) + \frac {32}{3} \, x^{3} \log \relax (5) + 1920 \, x^{3} \log \relax (x) + 2000 \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} - \frac {1588}{3} \, x^{3} + 4000 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x \log \relax (5) + 164 \, x^{2} \log \relax (5) + 5000 \, x^{2} \log \relax (x) + 2500 \, \log \relax (5) \log \relax (x)^{2} + 2500 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x - 1960 \, x^{2} + 8 \, {\left (4 \, x^{4} \log \relax (x) - x^{4}\right )} \log \relax (5) + \frac {1376}{9} \, {\left (3 \, x^{3} \log \relax (x) - x^{3}\right )} \log \relax (5) + 1360 \, {\left (2 \, x^{2} \log \relax (x) - x^{2}\right )} \log \relax (5) + 9000 \, {\left (x \log \relax (x) - x\right )} \log \relax (5) + 1040 \, x \log \relax (5) + 6000 \, x \log \relax (x) + 1000 \, \log \relax (5) \log \relax (x) - 4900 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^4+1920*x^3+4800*x^2+4000*x)*log(5)+320*x^5+2560*x^4+7200*x^3+8000*x^2+2500*x)*log(x)^2+((12
8*x^4+1376*x^3+5440*x^2+9000*x+5000)*log(5)+128*x^5+1408*x^4+5760*x^3+10000*x^2+6000*x)*log(x)+(32*x^3+328*x^2
+1040*x+1000)*log(5)+32*x^4+332*x^3+1080*x^2+1100*x)/x,x, algorithm="maxima")

[Out]

64/25*(25*log(x)^2 - 10*log(x) + 2)*x^5 + 8*(8*log(x)^2 - 4*log(x) + 1)*x^4*log(5) + 128/5*x^5*log(x) + 80*(8*
log(x)^2 - 4*log(x) + 1)*x^4 - 128/25*x^5 + 640/9*(9*log(x)^2 - 6*log(x) + 2)*x^3*log(5) + 352*x^4*log(x) + 80
0/3*(9*log(x)^2 - 6*log(x) + 2)*x^3 - 80*x^4 + 1200*(2*log(x)^2 - 2*log(x) + 1)*x^2*log(5) + 32/3*x^3*log(5) +
1920*x^3*log(x) + 2000*(2*log(x)^2 - 2*log(x) + 1)*x^2 - 1588/3*x^3 + 4000*(log(x)^2 - 2*log(x) + 2)*x*log(5)
+ 164*x^2*log(5) + 5000*x^2*log(x) + 2500*log(5)*log(x)^2 + 2500*(log(x)^2 - 2*log(x) + 2)*x - 1960*x^2 + 8*(
4*x^4*log(x) - x^4)*log(5) + 1376/9*(3*x^3*log(x) - x^3)*log(5) + 1360*(2*x^2*log(x) - x^2)*log(5) + 9000*(x*l
og(x) - x)*log(5) + 1040*x*log(5) + 6000*x*log(x) + 1000*log(5)*log(x) - 4900*x

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mupad [B]  time = 5.54, size = 126, normalized size = 6.00 \begin {gather*} 2500\,\ln \relax (5)\,{\ln \relax (x)}^2+x\,\left (\left (4000\,\ln \relax (5)+2500\right )\,{\ln \relax (x)}^2+\left (1000\,\ln \relax (5)+1000\right )\,\ln \relax (x)+40\,\ln \relax (5)+100\right )+x^2\,\left (\left (2400\,\ln \relax (5)+4000\right )\,{\ln \relax (x)}^2+\left (320\,\ln \relax (5)+1000\right )\,\ln \relax (x)+\ln \left (625\right )+40\right )+64\,x^5\,{\ln \relax (x)}^2+x^4\,\left (\left (64\,\ln \relax (5)+640\right )\,{\ln \relax (x)}^2+32\,\ln \relax (x)\right )+1000\,\ln \relax (5)\,\ln \relax (x)+x^3\,\left (\left (640\,\ln \relax (5)+2400\right )\,{\ln \relax (x)}^2+\left (32\,\ln \relax (5)+320\right )\,\ln \relax (x)+4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1100*x + log(x)^2*(2500*x + log(5)*(4000*x + 4800*x^2 + 1920*x^3 + 256*x^4) + 8000*x^2 + 7200*x^3 + 2560*
x^4 + 320*x^5) + log(5)*(1040*x + 328*x^2 + 32*x^3 + 1000) + 1080*x^2 + 332*x^3 + 32*x^4 + log(x)*(6000*x + lo
g(5)*(9000*x + 5440*x^2 + 1376*x^3 + 128*x^4 + 5000) + 10000*x^2 + 5760*x^3 + 1408*x^4 + 128*x^5))/x,x)

[Out]

2500*log(5)*log(x)^2 + x*(40*log(5) + log(x)*(1000*log(5) + 1000) + log(x)^2*(4000*log(5) + 2500) + 100) + x^2
*(log(625) + log(x)*(320*log(5) + 1000) + log(x)^2*(2400*log(5) + 4000) + 40) + 64*x^5*log(x)^2 + x^4*(32*log(
x) + log(x)^2*(64*log(5) + 640)) + 1000*log(5)*log(x) + x^3*(log(x)*(32*log(5) + 320) + log(x)^2*(640*log(5) +
2400) + 4)

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sympy [B]  time = 0.39, size = 143, normalized size = 6.81 \begin {gather*} 4 x^{3} + x^{2} \left (4 \log {\relax (5 )} + 40\right ) + x \left (40 \log {\relax (5 )} + 100\right ) + \left (32 x^{4} + 32 x^{3} \log {\relax (5 )} + 320 x^{3} + 320 x^{2} \log {\relax (5 )} + 1000 x^{2} + 1000 x + 1000 x \log {\relax (5 )}\right ) \log {\relax (x )} + \left (64 x^{5} + 64 x^{4} \log {\relax (5 )} + 640 x^{4} + 640 x^{3} \log {\relax (5 )} + 2400 x^{3} + 2400 x^{2} \log {\relax (5 )} + 4000 x^{2} + 2500 x + 4000 x \log {\relax (5 )} + 2500 \log {\relax (5 )}\right ) \log {\relax (x )}^{2} + 1000 \log {\relax (5 )} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x**4+1920*x**3+4800*x**2+4000*x)*ln(5)+320*x**5+2560*x**4+7200*x**3+8000*x**2+2500*x)*ln(x)**
2+((128*x**4+1376*x**3+5440*x**2+9000*x+5000)*ln(5)+128*x**5+1408*x**4+5760*x**3+10000*x**2+6000*x)*ln(x)+(32*
x**3+328*x**2+1040*x+1000)*ln(5)+32*x**4+332*x**3+1080*x**2+1100*x)/x,x)

[Out]

4*x**3 + x**2*(4*log(5) + 40) + x*(40*log(5) + 100) + (32*x**4 + 32*x**3*log(5) + 320*x**3 + 320*x**2*log(5) +
1000*x**2 + 1000*x + 1000*x*log(5))*log(x) + (64*x**5 + 64*x**4*log(5) + 640*x**4 + 640*x**3*log(5) + 2400*x*
*3 + 2400*x**2*log(5) + 4000*x**2 + 2500*x + 4000*x*log(5) + 2500*log(5))*log(x)**2 + 1000*log(5)*log(x)

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