3.54.54 \(\int \frac {32 x^2+16 x^3+1026 x^4+1280 x^5+576 x^6+112 x^7+8 x^8+(-64 x-32 x^2-3076 x^3-4096 x^4-1920 x^5-384 x^6-28 x^7) \log (3)+(32+16 x+3074 x^2+4608 x^3+2304 x^4+480 x^5+36 x^6) \log ^2(3)+(-1024 x-2048 x^2-1152 x^3-256 x^4-20 x^5) \log ^3(3)+(256 x+192 x^2+48 x^3+4 x^4) \log ^4(3)+(2+64 x^2+48 x^3+8 x^4+(-64 x-64 x^2-12 x^3) \log (3)+(16 x+4 x^2) \log ^2(3)) \log (x)}{x} \, dx\)

Optimal. Leaf size=19 \[ \left ((4+x)^2 (x-\log (3))^2+\log (x)\right )^2 \]

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Rubi [B]  time = 0.33, antiderivative size = 279, normalized size of antiderivative = 14.68, number of steps used = 12, number of rules used = 7, integrand size = 216, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {14, 1583, 1620, 2357, 2301, 2304, 2295} \begin {gather*} x^8+4 x^7 (4-\log (3))+2 x^6 \left (48+3 \log ^2(3)-32 \log (3)\right )+4 x^5 (4-\log (3)) \left (16+\log ^2(3)-20 \log (3)\right )-\frac {x^4}{2}+\frac {1}{2} x^4 \left (513+2 \log ^4(3)-128 \log ^3(3)+1152 \log ^2(3)-2048 \log (3)\right )+2 x^4 \log (x)+\frac {16}{3} x^3 \left (1+2 \log ^4(3)-68 \log ^3(3)+288 \log ^2(3)-192 \log (3)\right )+4 x^3 (4-\log (3)) \log (x)-\frac {4}{3} x^3 (4-\log (3))+2 x^2 \left (16+\log ^2(3)-16 \log (3)\right ) \log (x)-x^2 \left (16+\log ^2(3)-16 \log (3)\right )+x^2 \left (16+32 \log ^4(3)-768 \log ^3(3)+1537 \log ^2(3)\right )+16 x \log ^2(3)+\log ^2(x)+32 \log ^2(3) \log (x)-\frac {4}{3} (x+4)^3 \log (3) \left (1-4 \log ^3(3)+16 \log ^2(3)\right )-16 x (4-\log (3)) \log (3) \log (x)+16 x (4-\log (3)) \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(32*x^2 + 16*x^3 + 1026*x^4 + 1280*x^5 + 576*x^6 + 112*x^7 + 8*x^8 + (-64*x - 32*x^2 - 3076*x^3 - 4096*x^4
- 1920*x^5 - 384*x^6 - 28*x^7)*Log[3] + (32 + 16*x + 3074*x^2 + 4608*x^3 + 2304*x^4 + 480*x^5 + 36*x^6)*Log[3
]^2 + (-1024*x - 2048*x^2 - 1152*x^3 - 256*x^4 - 20*x^5)*Log[3]^3 + (256*x + 192*x^2 + 48*x^3 + 4*x^4)*Log[3]^
4 + (2 + 64*x^2 + 48*x^3 + 8*x^4 + (-64*x - 64*x^2 - 12*x^3)*Log[3] + (16*x + 4*x^2)*Log[3]^2)*Log[x])/x,x]

[Out]

-1/2*x^4 + x^8 - (4*x^3*(4 - Log[3]))/3 + 4*x^7*(4 - Log[3]) + 16*x*(4 - Log[3])*Log[3] + 16*x*Log[3]^2 + 4*x^
5*(4 - Log[3])*(16 - 20*Log[3] + Log[3]^2) - x^2*(16 - 16*Log[3] + Log[3]^2) + 2*x^6*(48 - 32*Log[3] + 3*Log[3
]^2) - (4*(4 + x)^3*Log[3]*(1 + 16*Log[3]^2 - 4*Log[3]^3))/3 + (x^4*(513 - 2048*Log[3] + 1152*Log[3]^2 - 128*L
og[3]^3 + 2*Log[3]^4))/2 + (16*x^3*(1 - 192*Log[3] + 288*Log[3]^2 - 68*Log[3]^3 + 2*Log[3]^4))/3 + x^2*(16 + 1
537*Log[3]^2 - 768*Log[3]^3 + 32*Log[3]^4) + 2*x^4*Log[x] + 4*x^3*(4 - Log[3])*Log[x] - 16*x*(4 - Log[3])*Log[
3]*Log[x] + 32*Log[3]^2*Log[x] + 2*x^2*(16 - 16*Log[3] + Log[3]^2)*Log[x] + 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 1583

Int[(Px_)*(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_.))^(p_), x_Symbol] :> Simp[(Coeff[Px, x, n - m - 1]*(a + b*x^n)^(p
+ 1))/(b*n*(p + 1)), x] + Int[(Px - Coeff[Px, x, n - m - 1]*x^(n - m - 1))*x^m*(a + b*x^n)^p, x] /; FreeQ[{a,
b, m, n}, x] && PolyQ[Px, x] && IGtQ[p, 1] && IGtQ[n - m, 0] && NeQ[Coeff[Px, x, n - m - 1], 0]

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 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 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 {2 (4+x)^2 (x-\log (3))^2 \left (1+4 x^4+6 x^3 (4-\log (3))-8 x (4-\log (3)) \log (3)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right )\right )}{x}+\frac {2 \left (1+4 x^4+6 x^3 (4-\log (3))-8 x (4-\log (3)) \log (3)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right )\right ) \log (x)}{x}\right ) \, dx\\ &=2 \int \frac {(4+x)^2 (x-\log (3))^2 \left (1+4 x^4+6 x^3 (4-\log (3))-8 x (4-\log (3)) \log (3)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right )\right )}{x} \, dx+2 \int \frac {\left (1+4 x^4+6 x^3 (4-\log (3))-8 x (4-\log (3)) \log (3)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right )\right ) \log (x)}{x} \, dx\\ &=-\frac {4}{3} (4+x)^3 \log (3) \left (1+16 \log ^2(3)-4 \log ^3(3)\right )+2 \int \frac {(4+x)^2 \left (-x \left (-2 \log (3)-32 \log ^3(3)+8 \log ^4(3)\right )+(x-\log (3))^2 \left (1+4 x^4+6 x^3 (4-\log (3))-8 x (4-\log (3)) \log (3)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right )\right )\right )}{x} \, dx+2 \int \left (\frac {\log (x)}{x}+4 x^3 \log (x)+6 x^2 (4-\log (3)) \log (x)-8 (4-\log (3)) \log (3) \log (x)+2 x \left (16-16 \log (3)+\log ^2(3)\right ) \log (x)\right ) \, dx\\ &=-\frac {4}{3} (4+x)^3 \log (3) \left (1+16 \log ^2(3)-4 \log ^3(3)\right )+2 \int \left (4 x^7+14 x^6 (4-\log (3))+8 \log ^2(3)+\frac {16 \log ^2(3)}{x}+10 x^4 (4-\log (3)) \left (16-20 \log (3)+\log ^2(3)\right )+6 x^5 \left (48-32 \log (3)+3 \log ^2(3)\right )+x^3 \left (513-2048 \log (3)+1152 \log ^2(3)-128 \log ^3(3)+2 \log ^4(3)\right )+8 x^2 \left (1-192 \log (3)+288 \log ^2(3)-68 \log ^3(3)+2 \log ^4(3)\right )+x \left (16+1537 \log ^2(3)-768 \log ^3(3)+32 \log ^4(3)\right )\right ) \, dx+2 \int \frac {\log (x)}{x} \, dx+8 \int x^3 \log (x) \, dx+(12 (4-\log (3))) \int x^2 \log (x) \, dx-(16 (4-\log (3)) \log (3)) \int \log (x) \, dx+\left (4 \left (16-16 \log (3)+\log ^2(3)\right )\right ) \int x \log (x) \, dx\\ &=-\frac {x^4}{2}+x^8-\frac {4}{3} x^3 (4-\log (3))+4 x^7 (4-\log (3))+16 x (4-\log (3)) \log (3)+16 x \log ^2(3)+4 x^5 (4-\log (3)) \left (16-20 \log (3)+\log ^2(3)\right )-x^2 \left (16-16 \log (3)+\log ^2(3)\right )+2 x^6 \left (48-32 \log (3)+3 \log ^2(3)\right )-\frac {4}{3} (4+x)^3 \log (3) \left (1+16 \log ^2(3)-4 \log ^3(3)\right )+\frac {1}{2} x^4 \left (513-2048 \log (3)+1152 \log ^2(3)-128 \log ^3(3)+2 \log ^4(3)\right )+\frac {16}{3} x^3 \left (1-192 \log (3)+288 \log ^2(3)-68 \log ^3(3)+2 \log ^4(3)\right )+x^2 \left (16+1537 \log ^2(3)-768 \log ^3(3)+32 \log ^4(3)\right )+2 x^4 \log (x)+4 x^3 (4-\log (3)) \log (x)-16 x (4-\log (3)) \log (3) \log (x)+32 \log ^2(3) \log (x)+2 x^2 \left (16-16 \log (3)+\log ^2(3)\right ) \log (x)+\log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} \left ((4+x)^2 (x-\log (3))^2+\log (x)\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(32*x^2 + 16*x^3 + 1026*x^4 + 1280*x^5 + 576*x^6 + 112*x^7 + 8*x^8 + (-64*x - 32*x^2 - 3076*x^3 - 40
96*x^4 - 1920*x^5 - 384*x^6 - 28*x^7)*Log[3] + (32 + 16*x + 3074*x^2 + 4608*x^3 + 2304*x^4 + 480*x^5 + 36*x^6)
*Log[3]^2 + (-1024*x - 2048*x^2 - 1152*x^3 - 256*x^4 - 20*x^5)*Log[3]^3 + (256*x + 192*x^2 + 48*x^3 + 4*x^4)*L
og[3]^4 + (2 + 64*x^2 + 48*x^3 + 8*x^4 + (-64*x - 64*x^2 - 12*x^3)*Log[3] + (16*x + 4*x^2)*Log[3]^2)*Log[x])/x
,x]

[Out]

((4 + x)^2*(x - Log[3])^2 + Log[x])^2

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fricas [B]  time = 0.78, size = 183, normalized size = 9.63 \begin {gather*} x^{8} + 16 \, x^{7} + 96 \, x^{6} + 256 \, x^{5} + {\left (x^{4} + 16 \, x^{3} + 96 \, x^{2} + 256 \, x\right )} \log \relax (3)^{4} + 256 \, x^{4} - 4 \, {\left (x^{5} + 16 \, x^{4} + 96 \, x^{3} + 256 \, x^{2} + 256 \, x\right )} \log \relax (3)^{3} + 6 \, {\left (x^{6} + 16 \, x^{5} + 96 \, x^{4} + 256 \, x^{3} + 256 \, x^{2}\right )} \log \relax (3)^{2} - 4 \, {\left (x^{7} + 16 \, x^{6} + 96 \, x^{5} + 256 \, x^{4} + 256 \, x^{3}\right )} \log \relax (3) + 2 \, {\left (x^{4} + 8 \, x^{3} + {\left (x^{2} + 8 \, x + 16\right )} \log \relax (3)^{2} + 16 \, x^{2} - 2 \, {\left (x^{3} + 8 \, x^{2} + 16 \, x\right )} \log \relax (3)\right )} \log \relax (x) + \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2+16*x)*log(3)^2+(-12*x^3-64*x^2-64*x)*log(3)+8*x^4+48*x^3+64*x^2+2)*log(x)+(4*x^4+48*x^3+192
*x^2+256*x)*log(3)^4+(-20*x^5-256*x^4-1152*x^3-2048*x^2-1024*x)*log(3)^3+(36*x^6+480*x^5+2304*x^4+4608*x^3+307
4*x^2+16*x+32)*log(3)^2+(-28*x^7-384*x^6-1920*x^5-4096*x^4-3076*x^3-32*x^2-64*x)*log(3)+8*x^8+112*x^7+576*x^6+
1280*x^5+1026*x^4+16*x^3+32*x^2)/x,x, algorithm="fricas")

[Out]

x^8 + 16*x^7 + 96*x^6 + 256*x^5 + (x^4 + 16*x^3 + 96*x^2 + 256*x)*log(3)^4 + 256*x^4 - 4*(x^5 + 16*x^4 + 96*x^
3 + 256*x^2 + 256*x)*log(3)^3 + 6*(x^6 + 16*x^5 + 96*x^4 + 256*x^3 + 256*x^2)*log(3)^2 - 4*(x^7 + 16*x^6 + 96*
x^5 + 256*x^4 + 256*x^3)*log(3) + 2*(x^4 + 8*x^3 + (x^2 + 8*x + 16)*log(3)^2 + 16*x^2 - 2*(x^3 + 8*x^2 + 16*x)
*log(3))*log(x) + log(x)^2

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giac [B]  time = 0.21, size = 196, normalized size = 10.32 \begin {gather*} x^{8} - 4 \, x^{7} {\left (\log \relax (3) - 4\right )} + 2 \, {\left (3 \, \log \relax (3)^{2} - 32 \, \log \relax (3) + 48\right )} x^{6} - 4 \, {\left (\log \relax (3)^{3} - 24 \, \log \relax (3)^{2} + 96 \, \log \relax (3) - 64\right )} x^{5} + {\left (\log \relax (3)^{4} - 64 \, \log \relax (3)^{3} + 576 \, \log \relax (3)^{2} - 1024 \, \log \relax (3) + 256\right )} x^{4} + 16 \, {\left (\log \relax (3)^{4} - 24 \, \log \relax (3)^{3} + 96 \, \log \relax (3)^{2} - 64 \, \log \relax (3)\right )} x^{3} + 32 \, {\left (3 \, \log \relax (3)^{4} - 32 \, \log \relax (3)^{3} + 48 \, \log \relax (3)^{2}\right )} x^{2} + 32 \, \log \relax (3)^{2} \log \relax (x) + 256 \, {\left (\log \relax (3)^{4} - 4 \, \log \relax (3)^{3}\right )} x + 2 \, {\left (x^{4} - 2 \, x^{3} {\left (\log \relax (3) - 4\right )} + {\left (\log \relax (3)^{2} - 16 \, \log \relax (3) + 16\right )} x^{2} + 8 \, {\left (\log \relax (3)^{2} - 4 \, \log \relax (3)\right )} x\right )} \log \relax (x) + \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2+16*x)*log(3)^2+(-12*x^3-64*x^2-64*x)*log(3)+8*x^4+48*x^3+64*x^2+2)*log(x)+(4*x^4+48*x^3+192
*x^2+256*x)*log(3)^4+(-20*x^5-256*x^4-1152*x^3-2048*x^2-1024*x)*log(3)^3+(36*x^6+480*x^5+2304*x^4+4608*x^3+307
4*x^2+16*x+32)*log(3)^2+(-28*x^7-384*x^6-1920*x^5-4096*x^4-3076*x^3-32*x^2-64*x)*log(3)+8*x^8+112*x^7+576*x^6+
1280*x^5+1026*x^4+16*x^3+32*x^2)/x,x, algorithm="giac")

[Out]

x^8 - 4*x^7*(log(3) - 4) + 2*(3*log(3)^2 - 32*log(3) + 48)*x^6 - 4*(log(3)^3 - 24*log(3)^2 + 96*log(3) - 64)*x
^5 + (log(3)^4 - 64*log(3)^3 + 576*log(3)^2 - 1024*log(3) + 256)*x^4 + 16*(log(3)^4 - 24*log(3)^3 + 96*log(3)^
2 - 64*log(3))*x^3 + 32*(3*log(3)^4 - 32*log(3)^3 + 48*log(3)^2)*x^2 + 32*log(3)^2*log(x) + 256*(log(3)^4 - 4*
log(3)^3)*x + 2*(x^4 - 2*x^3*(log(3) - 4) + (log(3)^2 - 16*log(3) + 16)*x^2 + 8*(log(3)^2 - 4*log(3))*x)*log(x
) + log(x)^2

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maple [B]  time = 0.07, size = 208, normalized size = 10.95

method	result	size
norman	\(x^{8}+\ln \relax (x )^{2}+32 \ln \relax (3)^{2} \ln \relax (x )+\left (256 \ln \relax (3)^{4}-1024 \ln \relax (3)^{3}\right ) x +\left (-4 \ln \relax (3)+16\right ) x^{7}+\left (6 \ln \relax (3)^{2}-64 \ln \relax (3)+96\right ) x^{6}+\left (1536 \ln \relax (3)^{2}+96 \ln \relax (3)^{4}-1024 \ln \relax (3)^{3}\right ) x^{2}+\left (-4 \ln \relax (3)^{3}+96 \ln \relax (3)^{2}-384 \ln \relax (3)+256\right ) x^{5}+\left (-1024 \ln \relax (3)+16 \ln \relax (3)^{4}-384 \ln \relax (3)^{3}+1536 \ln \relax (3)^{2}\right ) x^{3}+\left (256+\ln \relax (3)^{4}-64 \ln \relax (3)^{3}+576 \ln \relax (3)^{2}-1024 \ln \relax (3)\right ) x^{4}+\left (16 \ln \relax (3)^{2}-64 \ln \relax (3)\right ) x \ln \relax (x )+\left (-4 \ln \relax (3)+16\right ) x^{3} \ln \relax (x )+\left (2 \ln \relax (3)^{2}-32 \ln \relax (3)+32\right ) x^{2} \ln \relax (x )+2 x^{4} \ln \relax (x )\)	\(208\)
risch	\(-384 x^{3} \ln \relax (3)^{3}+16 x^{7}+x^{8}+\ln \relax (x )^{2}+256 x^{4}+96 x^{6}+256 x^{5}-64 x^{6} \ln \relax (3)-1024 x \ln \relax (3)^{3}+1536 x^{3} \ln \relax (3)^{2}+32 \ln \relax (3)^{2} \ln \relax (x )-384 x^{5} \ln \relax (3)-1024 x^{3} \ln \relax (3)+256 x \ln \relax (3)^{4}-1024 \ln \relax (3)^{3} x^{2}+x^{4} \ln \relax (3)^{4}+96 x^{2} \ln \relax (3)^{4}+96 x^{5} \ln \relax (3)^{2}+6 x^{6} \ln \relax (3)^{2}+1536 x^{2} \ln \relax (3)^{2}+576 x^{4} \ln \relax (3)^{2}-64 x^{4} \ln \relax (3)^{3}-1024 x^{4} \ln \relax (3)-4 \ln \relax (3)^{3} x^{5}-4 \ln \relax (3) x^{7}+16 \ln \relax (3)^{4} x^{3}+\left (2 x^{2} \ln \relax (3)^{2}-4 x^{3} \ln \relax (3)+2 x^{4}+16 x \ln \relax (3)^{2}-32 x^{2} \ln \relax (3)+16 x^{3}-64 x \ln \relax (3)+32 x^{2}\right ) \ln \relax (x )\)	\(247\)
default	\(32 x^{2} \ln \relax (x )-384 x^{3} \ln \relax (3)^{3}-16 x^{2} \ln \relax (3)+16 x^{7}+x^{8}+\ln \relax (x )^{2}+256 x^{4}+96 x^{6}+256 x^{5}+16 x^{3} \ln \relax (x )-64 x^{6} \ln \relax (3)-1024 x \ln \relax (3)^{3}+1536 x^{3} \ln \relax (3)^{2}+32 \ln \relax (3)^{2} \ln \relax (x )-384 x^{5} \ln \relax (3)-\frac {3076 x^{3} \ln \relax (3)}{3}+16 x \ln \relax (3)^{2}-64 x \ln \relax (3)+2 x^{4} \ln \relax (x )+256 x \ln \relax (3)^{4}-1024 \ln \relax (3)^{3} x^{2}+x^{4} \ln \relax (3)^{4}+96 x^{2} \ln \relax (3)^{4}+96 x^{5} \ln \relax (3)^{2}+6 x^{6} \ln \relax (3)^{2}+1537 x^{2} \ln \relax (3)^{2}+576 x^{4} \ln \relax (3)^{2}-64 x^{4} \ln \relax (3)^{3}-1024 x^{4} \ln \relax (3)-64 \ln \relax (3) \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )-12 \ln \relax (3) \left (\frac {x^{3} \ln \relax (x )}{3}-\frac {x^{3}}{9}\right )+16 \ln \relax (3)^{2} \left (x \ln \relax (x )-x \right )-64 \ln \relax (3) \left (x \ln \relax (x )-x \right )-4 \ln \relax (3)^{3} x^{5}-4 \ln \relax (3) x^{7}+16 \ln \relax (3)^{4} x^{3}+4 \ln \relax (3)^{2} \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )\)	\(312\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^2+16*x)*ln(3)^2+(-12*x^3-64*x^2-64*x)*ln(3)+8*x^4+48*x^3+64*x^2+2)*ln(x)+(4*x^4+48*x^3+192*x^2+256*
x)*ln(3)^4+(-20*x^5-256*x^4-1152*x^3-2048*x^2-1024*x)*ln(3)^3+(36*x^6+480*x^5+2304*x^4+4608*x^3+3074*x^2+16*x+
32)*ln(3)^2+(-28*x^7-384*x^6-1920*x^5-4096*x^4-3076*x^3-32*x^2-64*x)*ln(3)+8*x^8+112*x^7+576*x^6+1280*x^5+1026
*x^4+16*x^3+32*x^2)/x,x,method=_RETURNVERBOSE)

[Out]

x^8+ln(x)^2+32*ln(3)^2*ln(x)+(256*ln(3)^4-1024*ln(3)^3)*x+(-4*ln(3)+16)*x^7+(6*ln(3)^2-64*ln(3)+96)*x^6+(1536*
ln(3)^2+96*ln(3)^4-1024*ln(3)^3)*x^2+(-4*ln(3)^3+96*ln(3)^2-384*ln(3)+256)*x^5+(-1024*ln(3)+16*ln(3)^4-384*ln(
3)^3+1536*ln(3)^2)*x^3+(256+ln(3)^4-64*ln(3)^3+576*ln(3)^2-1024*ln(3))*x^4+(16*ln(3)^2-64*ln(3))*x*ln(x)+(-4*l
n(3)+16)*x^3*ln(x)+(2*ln(3)^2-32*ln(3)+32)*x^2*ln(x)+2*x^4*ln(x)

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maxima [B]  time = 0.45, size = 310, normalized size = 16.32 \begin {gather*} x^{8} - 4 \, x^{7} \log \relax (3) + 6 \, x^{6} \log \relax (3)^{2} - 4 \, x^{5} \log \relax (3)^{3} + x^{4} \log \relax (3)^{4} + 16 \, x^{7} - 64 \, x^{6} \log \relax (3) + 96 \, x^{5} \log \relax (3)^{2} - 64 \, x^{4} \log \relax (3)^{3} + 16 \, x^{3} \log \relax (3)^{4} + 96 \, x^{6} - 384 \, x^{5} \log \relax (3) + 576 \, x^{4} \log \relax (3)^{2} - 384 \, x^{3} \log \relax (3)^{3} + 96 \, x^{2} \log \relax (3)^{4} + 256 \, x^{5} - 1024 \, x^{4} \log \relax (3) + 1536 \, x^{3} \log \relax (3)^{2} - 1024 \, x^{2} \log \relax (3)^{3} + 256 \, x \log \relax (3)^{4} + 2 \, x^{4} \log \relax (x) + 256 \, x^{4} - \frac {3076}{3} \, x^{3} \log \relax (3) + 1537 \, x^{2} \log \relax (3)^{2} - 1024 \, x \log \relax (3)^{3} + 16 \, x^{3} \log \relax (x) - 16 \, x^{2} \log \relax (3) + {\left (2 \, x^{2} \log \relax (x) - x^{2}\right )} \log \relax (3)^{2} + 16 \, {\left (x \log \relax (x) - x\right )} \log \relax (3)^{2} + 16 \, x \log \relax (3)^{2} + 32 \, x^{2} \log \relax (x) + 32 \, \log \relax (3)^{2} \log \relax (x) - \frac {4}{3} \, {\left (3 \, x^{3} \log \relax (x) - x^{3}\right )} \log \relax (3) - 16 \, {\left (2 \, x^{2} \log \relax (x) - x^{2}\right )} \log \relax (3) - 64 \, {\left (x \log \relax (x) - x\right )} \log \relax (3) - 64 \, x \log \relax (3) + \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^2+16*x)*log(3)^2+(-12*x^3-64*x^2-64*x)*log(3)+8*x^4+48*x^3+64*x^2+2)*log(x)+(4*x^4+48*x^3+192
*x^2+256*x)*log(3)^4+(-20*x^5-256*x^4-1152*x^3-2048*x^2-1024*x)*log(3)^3+(36*x^6+480*x^5+2304*x^4+4608*x^3+307
4*x^2+16*x+32)*log(3)^2+(-28*x^7-384*x^6-1920*x^5-4096*x^4-3076*x^3-32*x^2-64*x)*log(3)+8*x^8+112*x^7+576*x^6+
1280*x^5+1026*x^4+16*x^3+32*x^2)/x,x, algorithm="maxima")

[Out]

x^8 - 4*x^7*log(3) + 6*x^6*log(3)^2 - 4*x^5*log(3)^3 + x^4*log(3)^4 + 16*x^7 - 64*x^6*log(3) + 96*x^5*log(3)^2
- 64*x^4*log(3)^3 + 16*x^3*log(3)^4 + 96*x^6 - 384*x^5*log(3) + 576*x^4*log(3)^2 - 384*x^3*log(3)^3 + 96*x^2*
log(3)^4 + 256*x^5 - 1024*x^4*log(3) + 1536*x^3*log(3)^2 - 1024*x^2*log(3)^3 + 256*x*log(3)^4 + 2*x^4*log(x) +
256*x^4 - 3076/3*x^3*log(3) + 1537*x^2*log(3)^2 - 1024*x*log(3)^3 + 16*x^3*log(x) - 16*x^2*log(3) + (2*x^2*lo
g(x) - x^2)*log(3)^2 + 16*(x*log(x) - x)*log(3)^2 + 16*x*log(3)^2 + 32*x^2*log(x) + 32*log(3)^2*log(x) - 4/3*(
3*x^3*log(x) - x^3)*log(3) - 16*(2*x^2*log(x) - x^2)*log(3) - 64*(x*log(x) - x)*log(3) - 64*x*log(3) + log(x)^
2

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mupad [B]  time = 3.71, size = 184, normalized size = 9.68 \begin {gather*} 32\,{\ln \relax (3)}^2\,\ln \relax (x)-x^7\,\left (\ln \left (81\right )-16\right )+{\ln \relax (x)}^2+x^6\,\left (6\,{\ln \relax (3)}^2-64\,\ln \relax (3)+96\right )-x^3\,\left (\ln \relax (x)\,\left (\ln \left (81\right )-16\right )-16\,\ln \relax (3)\,\left (96\,\ln \relax (3)-24\,{\ln \relax (3)}^2+{\ln \relax (3)}^3-64\right )\right )+x\,\left (256\,{\ln \relax (3)}^3\,\left (\ln \relax (3)-4\right )+16\,\ln \relax (3)\,\ln \relax (x)\,\left (\ln \relax (3)-4\right )\right )+x^2\,\left (32\,{\ln \relax (3)}^2\,\left (3\,{\ln \relax (3)}^2-32\,\ln \relax (3)+48\right )+\ln \relax (x)\,\left (2\,{\ln \relax (3)}^2-32\,\ln \relax (3)+32\right )\right )+x^4\,\left (2\,\ln \relax (x)-1024\,\ln \relax (3)+576\,{\ln \relax (3)}^2-64\,{\ln \relax (3)}^3+{\ln \relax (3)}^4+256\right )+x^8-4\,x^5\,\left (\ln \relax (3)-4\right )\,\left ({\ln \relax (3)}^2-20\,\ln \relax (3)+16\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(3)^4*(256*x + 192*x^2 + 48*x^3 + 4*x^4) - log(3)^3*(1024*x + 2048*x^2 + 1152*x^3 + 256*x^4 + 20*x^5)
- log(3)*(64*x + 32*x^2 + 3076*x^3 + 4096*x^4 + 1920*x^5 + 384*x^6 + 28*x^7) + log(x)*(log(3)^2*(16*x + 4*x^2)
- log(3)*(64*x + 64*x^2 + 12*x^3) + 64*x^2 + 48*x^3 + 8*x^4 + 2) + log(3)^2*(16*x + 3074*x^2 + 4608*x^3 + 230
4*x^4 + 480*x^5 + 36*x^6 + 32) + 32*x^2 + 16*x^3 + 1026*x^4 + 1280*x^5 + 576*x^6 + 112*x^7 + 8*x^8)/x,x)

[Out]

32*log(3)^2*log(x) - x^7*(log(81) - 16) + log(x)^2 + x^6*(6*log(3)^2 - 64*log(3) + 96) - x^3*(log(x)*(log(81)
- 16) - 16*log(3)*(96*log(3) - 24*log(3)^2 + log(3)^3 - 64)) + x*(256*log(3)^3*(log(3) - 4) + 16*log(3)*log(x)
*(log(3) - 4)) + x^2*(32*log(3)^2*(3*log(3)^2 - 32*log(3) + 48) + log(x)*(2*log(3)^2 - 32*log(3) + 32)) + x^4*
(2*log(x) - 1024*log(3) + 576*log(3)^2 - 64*log(3)^3 + log(3)^4 + 256) + x^8 - 4*x^5*(log(3) - 4)*(log(3)^2 -
20*log(3) + 16)

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sympy [B]  time = 0.51, size = 226, normalized size = 11.89 \begin {gather*} x^{8} + x^{7} \left (16 - 4 \log {\relax (3 )}\right ) + x^{6} \left (- 64 \log {\relax (3 )} + 6 \log {\relax (3 )}^{2} + 96\right ) + x^{5} \left (- 384 \log {\relax (3 )} - 4 \log {\relax (3 )}^{3} + 96 \log {\relax (3 )}^{2} + 256\right ) + x^{4} \left (- 1024 \log {\relax (3 )} - 64 \log {\relax (3 )}^{3} + \log {\relax (3 )}^{4} + 256 + 576 \log {\relax (3 )}^{2}\right ) + x^{3} \left (- 1024 \log {\relax (3 )} - 384 \log {\relax (3 )}^{3} + 16 \log {\relax (3 )}^{4} + 1536 \log {\relax (3 )}^{2}\right ) + x^{2} \left (- 1024 \log {\relax (3 )}^{3} + 96 \log {\relax (3 )}^{4} + 1536 \log {\relax (3 )}^{2}\right ) + x \left (- 1024 \log {\relax (3 )}^{3} + 256 \log {\relax (3 )}^{4}\right ) + \left (2 x^{4} - 4 x^{3} \log {\relax (3 )} + 16 x^{3} - 32 x^{2} \log {\relax (3 )} + 2 x^{2} \log {\relax (3 )}^{2} + 32 x^{2} - 64 x \log {\relax (3 )} + 16 x \log {\relax (3 )}^{2}\right ) \log {\relax (x )} + \log {\relax (x )}^{2} + 32 \log {\relax (3 )}^{2} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**2+16*x)*ln(3)**2+(-12*x**3-64*x**2-64*x)*ln(3)+8*x**4+48*x**3+64*x**2+2)*ln(x)+(4*x**4+48*x*
*3+192*x**2+256*x)*ln(3)**4+(-20*x**5-256*x**4-1152*x**3-2048*x**2-1024*x)*ln(3)**3+(36*x**6+480*x**5+2304*x**
4+4608*x**3+3074*x**2+16*x+32)*ln(3)**2+(-28*x**7-384*x**6-1920*x**5-4096*x**4-3076*x**3-32*x**2-64*x)*ln(3)+8
*x**8+112*x**7+576*x**6+1280*x**5+1026*x**4+16*x**3+32*x**2)/x,x)

[Out]

x**8 + x**7*(16 - 4*log(3)) + x**6*(-64*log(3) + 6*log(3)**2 + 96) + x**5*(-384*log(3) - 4*log(3)**3 + 96*log(
3)**2 + 256) + x**4*(-1024*log(3) - 64*log(3)**3 + log(3)**4 + 256 + 576*log(3)**2) + x**3*(-1024*log(3) - 384
*log(3)**3 + 16*log(3)**4 + 1536*log(3)**2) + x**2*(-1024*log(3)**3 + 96*log(3)**4 + 1536*log(3)**2) + x*(-102
4*log(3)**3 + 256*log(3)**4) + (2*x**4 - 4*x**3*log(3) + 16*x**3 - 32*x**2*log(3) + 2*x**2*log(3)**2 + 32*x**2
- 64*x*log(3) + 16*x*log(3)**2)*log(x) + log(x)**2 + 32*log(3)**2*log(x)

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