3.62.65 \(\int \frac {(4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} (-3264 x-96 x^3)+e^{2/x} (848 x^2+8 x^4)) \log ^3(\frac {x}{16})+(136 x^2+4 x^4+e^{\frac {1}{x}} (816-816 x+24 x^2-72 x^3)+e^{3/x} (72 x^2-72 x^3)+e^{4/x} (-4 x^3+4 x^4)+e^{2/x} (-424 x+424 x^2-4 x^3+8 x^4)) \log ^4(\frac {x}{16})}{x} \, dx\)

Optimal. Leaf size=28 \[ \left (-2+x^2+\left (6-e^{\frac {1}{x}} x\right )^2\right )^2 \log ^4\left (\frac {x}{16}\right ) \]

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Rubi [B]  time = 1.05, antiderivative size = 138, normalized size of antiderivative = 4.93, number of steps used = 29, number of rules used = 9, integrand size = 190, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {14, 2288, 6742, 2353, 2302, 30, 2305, 2304, 2338} \begin {gather*} -e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (x^2+34\right )^2 \log ^4\left (\frac {x}{16}\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (x^2 \log \left (\frac {x}{16}\right )+106 \log \left (\frac {x}{16}\right )\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (x^2 \log \left (\frac {x}{16}\right )+34 \log \left (\frac {x}{16}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((4624 + 272*x^2 - 96*E^(3/x)*x^3 + 4*x^4 + 4*E^(4/x)*x^4 + E^x^(-1)*(-3264*x - 96*x^3) + E^(2/x)*(848*x^2
+ 8*x^4))*Log[x/16]^3 + (136*x^2 + 4*x^4 + E^x^(-1)*(816 - 816*x + 24*x^2 - 72*x^3) + E^(3/x)*(72*x^2 - 72*x^
3) + E^(4/x)*(-4*x^3 + 4*x^4) + E^(2/x)*(-424*x + 424*x^2 - 4*x^3 + 8*x^4))*Log[x/16]^4)/x,x]

[Out]

-24*E^(3/x)*x^3*Log[x/16]^4 + (34 + x^2)^2*Log[x/16]^4 - 24*E^x^(-1)*x*Log[x/16]^3*(34*Log[x/16] + x^2*Log[x/1
6]) + 2*E^(2/x)*x^2*Log[x/16]^3*(106*Log[x/16] + x^2*Log[x/16]) - E^(4/x)*x^4*Log[x/16]^3*(Log[16] - Log[x])

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 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rule 2302

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, 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 2338

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

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 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-24 e^{3/x} x \log ^3\left (\frac {x}{16}\right ) \left (4 x-3 \log \left (\frac {x}{16}\right )+3 x \log \left (\frac {x}{16}\right )\right )+\frac {4 \left (34+x^2\right ) \log ^3\left (\frac {x}{16}\right ) \left (34+x^2+x^2 \log \left (\frac {x}{16}\right )\right )}{x}+4 e^{2/x} \log ^3\left (\frac {x}{16}\right ) \left (212 x+2 x^3-106 \log \left (\frac {x}{16}\right )+106 x \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+2 x^3 \log \left (\frac {x}{16}\right )\right )-\frac {24 e^{\frac {1}{x}} \log ^3\left (\frac {x}{16}\right ) \left (136 x+4 x^3-34 \log \left (\frac {x}{16}\right )+34 x \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+3 x^3 \log \left (\frac {x}{16}\right )\right )}{x}+4 e^{4/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (x+\log (16)+x \log \left (\frac {x}{16}\right )-\log (x)\right )\right ) \, dx\\ &=4 \int \frac {\left (34+x^2\right ) \log ^3\left (\frac {x}{16}\right ) \left (34+x^2+x^2 \log \left (\frac {x}{16}\right )\right )}{x} \, dx+4 \int e^{2/x} \log ^3\left (\frac {x}{16}\right ) \left (212 x+2 x^3-106 \log \left (\frac {x}{16}\right )+106 x \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+2 x^3 \log \left (\frac {x}{16}\right )\right ) \, dx+4 \int e^{4/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (x+\log (16)+x \log \left (\frac {x}{16}\right )-\log (x)\right ) \, dx-24 \int e^{3/x} x \log ^3\left (\frac {x}{16}\right ) \left (4 x-3 \log \left (\frac {x}{16}\right )+3 x \log \left (\frac {x}{16}\right )\right ) \, dx-24 \int \frac {e^{\frac {1}{x}} \log ^3\left (\frac {x}{16}\right ) \left (136 x+4 x^3-34 \log \left (\frac {x}{16}\right )+34 x \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+3 x^3 \log \left (\frac {x}{16}\right )\right )}{x} \, dx\\ &=-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))+4 \int \left (\frac {\left (34+x^2\right )^2 \log ^3\left (\frac {x}{16}\right )}{x}+x \left (34+x^2\right ) \log ^4\left (\frac {x}{16}\right )\right ) \, dx\\ &=-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))+4 \int \frac {\left (34+x^2\right )^2 \log ^3\left (\frac {x}{16}\right )}{x} \, dx+4 \int x \left (34+x^2\right ) \log ^4\left (\frac {x}{16}\right ) \, dx\\ &=-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))-4 \int \frac {\left (34+x^2\right )^2 \log ^3\left (\frac {x}{16}\right )}{x} \, dx+4 \int \left (\frac {1156 \log ^3\left (\frac {x}{16}\right )}{x}+68 x \log ^3\left (\frac {x}{16}\right )+x^3 \log ^3\left (\frac {x}{16}\right )\right ) \, dx\\ &=-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))+4 \int x^3 \log ^3\left (\frac {x}{16}\right ) \, dx-4 \int \left (\frac {1156 \log ^3\left (\frac {x}{16}\right )}{x}+68 x \log ^3\left (\frac {x}{16}\right )+x^3 \log ^3\left (\frac {x}{16}\right )\right ) \, dx+272 \int x \log ^3\left (\frac {x}{16}\right ) \, dx+4624 \int \frac {\log ^3\left (\frac {x}{16}\right )}{x} \, dx\\ &=136 x^2 \log ^3\left (\frac {x}{16}\right )+x^4 \log ^3\left (\frac {x}{16}\right )-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))-3 \int x^3 \log ^2\left (\frac {x}{16}\right ) \, dx-4 \int x^3 \log ^3\left (\frac {x}{16}\right ) \, dx-272 \int x \log ^3\left (\frac {x}{16}\right ) \, dx-408 \int x \log ^2\left (\frac {x}{16}\right ) \, dx-4624 \int \frac {\log ^3\left (\frac {x}{16}\right )}{x} \, dx+4624 \operatorname {Subst}\left (\int x^3 \, dx,x,\log \left (\frac {x}{16}\right )\right )\\ &=-204 x^2 \log ^2\left (\frac {x}{16}\right )-\frac {3}{4} x^4 \log ^2\left (\frac {x}{16}\right )+1156 \log ^4\left (\frac {x}{16}\right )-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))+\frac {3}{2} \int x^3 \log \left (\frac {x}{16}\right ) \, dx+3 \int x^3 \log ^2\left (\frac {x}{16}\right ) \, dx+408 \int x \log \left (\frac {x}{16}\right ) \, dx+408 \int x \log ^2\left (\frac {x}{16}\right ) \, dx-4624 \operatorname {Subst}\left (\int x^3 \, dx,x,\log \left (\frac {x}{16}\right )\right )\\ &=-102 x^2-\frac {3 x^4}{32}+204 x^2 \log \left (\frac {x}{16}\right )+\frac {3}{8} x^4 \log \left (\frac {x}{16}\right )-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))-\frac {3}{2} \int x^3 \log \left (\frac {x}{16}\right ) \, dx-408 \int x \log \left (\frac {x}{16}\right ) \, dx\\ &=-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (34+x^2\right )^2 \log ^4\left (\frac {x}{16}\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (34 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (106 \log \left (\frac {x}{16}\right )+x^2 \log \left (\frac {x}{16}\right )\right )-e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 35, normalized size = 1.25 \begin {gather*} \left (34-12 e^{\frac {1}{x}} x+x^2+e^{2/x} x^2\right )^2 \log ^4\left (\frac {x}{16}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((4624 + 272*x^2 - 96*E^(3/x)*x^3 + 4*x^4 + 4*E^(4/x)*x^4 + E^x^(-1)*(-3264*x - 96*x^3) + E^(2/x)*(8
48*x^2 + 8*x^4))*Log[x/16]^3 + (136*x^2 + 4*x^4 + E^x^(-1)*(816 - 816*x + 24*x^2 - 72*x^3) + E^(3/x)*(72*x^2 -
72*x^3) + E^(4/x)*(-4*x^3 + 4*x^4) + E^(2/x)*(-424*x + 424*x^2 - 4*x^3 + 8*x^4))*Log[x/16]^4)/x,x]

[Out]

(34 - 12*E^x^(-1)*x + x^2 + E^(2/x)*x^2)^2*Log[x/16]^4

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fricas [B]  time = 0.61, size = 68, normalized size = 2.43 \begin {gather*} {\left (x^{4} e^{\frac {4}{x}} + x^{4} - 24 \, x^{3} e^{\frac {3}{x}} + 68 \, x^{2} + 2 \, {\left (x^{4} + 106 \, x^{2}\right )} e^{\frac {2}{x}} - 24 \, {\left (x^{3} + 34 \, x\right )} e^{\frac {1}{x}} + 1156\right )} \log \left (\frac {1}{16} \, x\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4*x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x
^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+136*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)
*exp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x, algorithm="fricas")

[Out]

(x^4*e^(4/x) + x^4 - 24*x^3*e^(3/x) + 68*x^2 + 2*(x^4 + 106*x^2)*e^(2/x) - 24*(x^3 + 34*x)*e^(1/x) + 1156)*log
(1/16*x)^4

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giac [B]  time = 0.33, size = 605, normalized size = 21.61 \begin {gather*} 256 \, x^{4} e^{\frac {4}{x}} \log \relax (2)^{4} + 512 \, x^{4} e^{\frac {2}{x}} \log \relax (2)^{4} - 256 \, x^{4} e^{\frac {4}{x}} \log \relax (2)^{3} \log \relax (x) - 512 \, x^{4} e^{\frac {2}{x}} \log \relax (2)^{3} \log \relax (x) + 96 \, x^{4} e^{\frac {4}{x}} \log \relax (2)^{2} \log \relax (x)^{2} + 192 \, x^{4} e^{\frac {2}{x}} \log \relax (2)^{2} \log \relax (x)^{2} - 16 \, x^{4} e^{\frac {4}{x}} \log \relax (2) \log \relax (x)^{3} - 32 \, x^{4} e^{\frac {2}{x}} \log \relax (2) \log \relax (x)^{3} + x^{4} e^{\frac {4}{x}} \log \relax (x)^{4} + 2 \, x^{4} e^{\frac {2}{x}} \log \relax (x)^{4} + 256 \, x^{4} \log \relax (2)^{4} - 6144 \, x^{3} e^{\frac {3}{x}} \log \relax (2)^{4} - 6144 \, x^{3} e^{\frac {1}{x}} \log \relax (2)^{4} - 256 \, x^{4} \log \relax (2)^{3} \log \relax (x) + 6144 \, x^{3} e^{\frac {3}{x}} \log \relax (2)^{3} \log \relax (x) + 6144 \, x^{3} e^{\frac {1}{x}} \log \relax (2)^{3} \log \relax (x) + 96 \, x^{4} \log \relax (2)^{2} \log \relax (x)^{2} - 2304 \, x^{3} e^{\frac {3}{x}} \log \relax (2)^{2} \log \relax (x)^{2} - 2304 \, x^{3} e^{\frac {1}{x}} \log \relax (2)^{2} \log \relax (x)^{2} - 16 \, x^{4} \log \relax (2) \log \relax (x)^{3} + 384 \, x^{3} e^{\frac {3}{x}} \log \relax (2) \log \relax (x)^{3} + 384 \, x^{3} e^{\frac {1}{x}} \log \relax (2) \log \relax (x)^{3} + x^{4} \log \relax (x)^{4} - 24 \, x^{3} e^{\frac {3}{x}} \log \relax (x)^{4} - 24 \, x^{3} e^{\frac {1}{x}} \log \relax (x)^{4} + 54272 \, x^{2} e^{\frac {2}{x}} \log \relax (2)^{4} - 54272 \, x^{2} e^{\frac {2}{x}} \log \relax (2)^{3} \log \relax (x) + 20352 \, x^{2} e^{\frac {2}{x}} \log \relax (2)^{2} \log \relax (x)^{2} - 3392 \, x^{2} e^{\frac {2}{x}} \log \relax (2) \log \relax (x)^{3} + 212 \, x^{2} e^{\frac {2}{x}} \log \relax (x)^{4} + 17408 \, x^{2} \log \relax (2)^{4} - 208896 \, x e^{\frac {1}{x}} \log \relax (2)^{4} - 17408 \, x^{2} \log \relax (2)^{3} \log \relax (x) + 208896 \, x e^{\frac {1}{x}} \log \relax (2)^{3} \log \relax (x) + 6528 \, x^{2} \log \relax (2)^{2} \log \relax (x)^{2} - 78336 \, x e^{\frac {1}{x}} \log \relax (2)^{2} \log \relax (x)^{2} - 1088 \, x^{2} \log \relax (2) \log \relax (x)^{3} + 13056 \, x e^{\frac {1}{x}} \log \relax (2) \log \relax (x)^{3} + 68 \, x^{2} \log \relax (x)^{4} - 816 \, x e^{\frac {1}{x}} \log \relax (x)^{4} - 295936 \, \log \relax (2)^{3} \log \relax (x) + 110976 \, \log \relax (2)^{2} \log \relax (x)^{2} - 18496 \, \log \relax (2) \log \relax (x)^{3} + 1156 \, \log \relax (x)^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4*x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x
^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+136*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)
*exp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x, algorithm="giac")

[Out]

256*x^4*e^(4/x)*log(2)^4 + 512*x^4*e^(2/x)*log(2)^4 - 256*x^4*e^(4/x)*log(2)^3*log(x) - 512*x^4*e^(2/x)*log(2)
^3*log(x) + 96*x^4*e^(4/x)*log(2)^2*log(x)^2 + 192*x^4*e^(2/x)*log(2)^2*log(x)^2 - 16*x^4*e^(4/x)*log(2)*log(x
)^3 - 32*x^4*e^(2/x)*log(2)*log(x)^3 + x^4*e^(4/x)*log(x)^4 + 2*x^4*e^(2/x)*log(x)^4 + 256*x^4*log(2)^4 - 6144
*x^3*e^(3/x)*log(2)^4 - 6144*x^3*e^(1/x)*log(2)^4 - 256*x^4*log(2)^3*log(x) + 6144*x^3*e^(3/x)*log(2)^3*log(x)
+ 6144*x^3*e^(1/x)*log(2)^3*log(x) + 96*x^4*log(2)^2*log(x)^2 - 2304*x^3*e^(3/x)*log(2)^2*log(x)^2 - 2304*x^3
*e^(1/x)*log(2)^2*log(x)^2 - 16*x^4*log(2)*log(x)^3 + 384*x^3*e^(3/x)*log(2)*log(x)^3 + 384*x^3*e^(1/x)*log(2)
*log(x)^3 + x^4*log(x)^4 - 24*x^3*e^(3/x)*log(x)^4 - 24*x^3*e^(1/x)*log(x)^4 + 54272*x^2*e^(2/x)*log(2)^4 - 54
272*x^2*e^(2/x)*log(2)^3*log(x) + 20352*x^2*e^(2/x)*log(2)^2*log(x)^2 - 3392*x^2*e^(2/x)*log(2)*log(x)^3 + 212
*x^2*e^(2/x)*log(x)^4 + 17408*x^2*log(2)^4 - 208896*x*e^(1/x)*log(2)^4 - 17408*x^2*log(2)^3*log(x) + 208896*x*
e^(1/x)*log(2)^3*log(x) + 6528*x^2*log(2)^2*log(x)^2 - 78336*x*e^(1/x)*log(2)^2*log(x)^2 - 1088*x^2*log(2)*log
(x)^3 + 13056*x*e^(1/x)*log(2)*log(x)^3 + 68*x^2*log(x)^4 - 816*x*e^(1/x)*log(x)^4 - 295936*log(2)^3*log(x) +
110976*log(2)^2*log(x)^2 - 18496*log(2)*log(x)^3 + 1156*log(x)^4

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maple [B]  time = 1.20, size = 77, normalized size = 2.75

method	result	size
risch	\(\left (x^{4} {\mathrm e}^{\frac {4}{x}}+2 \,{\mathrm e}^{\frac {2}{x}} x^{4}-24 x^{3} {\mathrm e}^{\frac {3}{x}}+x^{4}-24 x^{3} {\mathrm e}^{\frac {1}{x}}+212 x^{2} {\mathrm e}^{\frac {2}{x}}+68 x^{2}-816 x \,{\mathrm e}^{\frac {1}{x}}+1156\right ) \ln \left (\frac {x}{16}\right )^{4}\)	\(77\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4*x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x^3+24*
x^2-816*x+816)*exp(1/x)+4*x^4+136*x^2)*ln(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)*exp(1/
x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*ln(1/16*x)^3)/x,x,method=_RETURNVERBOSE)

[Out]

(x^4*exp(4/x)+2*exp(2/x)*x^4-24*x^3*exp(3/x)+x^4-24*x^3*exp(1/x)+212*x^2*exp(2/x)+68*x^2-816*x*exp(1/x)+1156)*
ln(1/16*x)^4

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maxima [B]  time = 0.50, size = 464, normalized size = 16.57 \begin {gather*} \frac {1}{32} \, {\left (32 \, \log \left (\frac {1}{16} \, x\right )^{4} - 32 \, \log \left (\frac {1}{16} \, x\right )^{3} + 24 \, \log \left (\frac {1}{16} \, x\right )^{2} - 12 \, \log \left (\frac {1}{16} \, x\right ) + 3\right )} x^{4} + \frac {1}{32} \, {\left (32 \, \log \left (\frac {1}{16} \, x\right )^{3} - 24 \, \log \left (\frac {1}{16} \, x\right )^{2} + 12 \, \log \left (\frac {1}{16} \, x\right ) - 3\right )} x^{4} + 1156 \, \log \left (\frac {1}{16} \, x\right )^{4} + 34 \, {\left (2 \, \log \left (\frac {1}{16} \, x\right )^{4} - 4 \, \log \left (\frac {1}{16} \, x\right )^{3} + 6 \, \log \left (\frac {1}{16} \, x\right )^{2} - 6 \, \log \left (\frac {1}{16} \, x\right ) + 3\right )} x^{2} + 34 \, {\left (4 \, \log \left (\frac {1}{16} \, x\right )^{3} - 6 \, \log \left (\frac {1}{16} \, x\right )^{2} + 6 \, \log \left (\frac {1}{16} \, x\right ) - 3\right )} x^{2} + {\left (256 \, x^{4} \log \relax (2)^{4} - 256 \, x^{4} \log \relax (2)^{3} \log \relax (x) + 96 \, x^{4} \log \relax (2)^{2} \log \relax (x)^{2} - 16 \, x^{4} \log \relax (2) \log \relax (x)^{3} + x^{4} \log \relax (x)^{4}\right )} e^{\frac {4}{x}} - 24 \, {\left (256 \, x^{3} \log \relax (2)^{4} - 256 \, x^{3} \log \relax (2)^{3} \log \relax (x) + 96 \, x^{3} \log \relax (2)^{2} \log \relax (x)^{2} - 16 \, x^{3} \log \relax (2) \log \relax (x)^{3} + x^{3} \log \relax (x)^{4}\right )} e^{\frac {3}{x}} + 2 \, {\left (256 \, x^{4} \log \relax (2)^{4} + 27136 \, x^{2} \log \relax (2)^{4} + {\left (x^{4} + 106 \, x^{2}\right )} \log \relax (x)^{4} - 16 \, {\left (x^{4} \log \relax (2) + 106 \, x^{2} \log \relax (2)\right )} \log \relax (x)^{3} + 96 \, {\left (x^{4} \log \relax (2)^{2} + 106 \, x^{2} \log \relax (2)^{2}\right )} \log \relax (x)^{2} - 256 \, {\left (x^{4} \log \relax (2)^{3} + 106 \, x^{2} \log \relax (2)^{3}\right )} \log \relax (x)\right )} e^{\frac {2}{x}} - 24 \, {\left (256 \, x^{3} \log \relax (2)^{4} + 8704 \, x \log \relax (2)^{4} + {\left (x^{3} + 34 \, x\right )} \log \relax (x)^{4} - 16 \, {\left (x^{3} \log \relax (2) + 34 \, x \log \relax (2)\right )} \log \relax (x)^{3} + 96 \, {\left (x^{3} \log \relax (2)^{2} + 34 \, x \log \relax (2)^{2}\right )} \log \relax (x)^{2} - 256 \, {\left (x^{3} \log \relax (2)^{3} + 34 \, x \log \relax (2)^{3}\right )} \log \relax (x)\right )} e^{\frac {1}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4*x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x
^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+136*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)
*exp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x, algorithm="maxima")

[Out]

1/32*(32*log(1/16*x)^4 - 32*log(1/16*x)^3 + 24*log(1/16*x)^2 - 12*log(1/16*x) + 3)*x^4 + 1/32*(32*log(1/16*x)^
3 - 24*log(1/16*x)^2 + 12*log(1/16*x) - 3)*x^4 + 1156*log(1/16*x)^4 + 34*(2*log(1/16*x)^4 - 4*log(1/16*x)^3 +
6*log(1/16*x)^2 - 6*log(1/16*x) + 3)*x^2 + 34*(4*log(1/16*x)^3 - 6*log(1/16*x)^2 + 6*log(1/16*x) - 3)*x^2 + (2
56*x^4*log(2)^4 - 256*x^4*log(2)^3*log(x) + 96*x^4*log(2)^2*log(x)^2 - 16*x^4*log(2)*log(x)^3 + x^4*log(x)^4)*
e^(4/x) - 24*(256*x^3*log(2)^4 - 256*x^3*log(2)^3*log(x) + 96*x^3*log(2)^2*log(x)^2 - 16*x^3*log(2)*log(x)^3 +
x^3*log(x)^4)*e^(3/x) + 2*(256*x^4*log(2)^4 + 27136*x^2*log(2)^4 + (x^4 + 106*x^2)*log(x)^4 - 16*(x^4*log(2)
+ 106*x^2*log(2))*log(x)^3 + 96*(x^4*log(2)^2 + 106*x^2*log(2)^2)*log(x)^2 - 256*(x^4*log(2)^3 + 106*x^2*log(2
)^3)*log(x))*e^(2/x) - 24*(256*x^3*log(2)^4 + 8704*x*log(2)^4 + (x^3 + 34*x)*log(x)^4 - 16*(x^3*log(2) + 34*x*
log(2))*log(x)^3 + 96*(x^3*log(2)^2 + 34*x*log(2)^2)*log(x)^2 - 256*(x^3*log(2)^3 + 34*x*log(2)^3)*log(x))*e^(
1/x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \left (\frac {x}{16}\right )}^3\,\left ({\mathrm {e}}^{2/x}\,\left (8\,x^4+848\,x^2\right )-{\mathrm {e}}^{1/x}\,\left (96\,x^3+3264\,x\right )-96\,x^3\,{\mathrm {e}}^{3/x}+4\,x^4\,{\mathrm {e}}^{4/x}+272\,x^2+4\,x^4+4624\right )-{\ln \left (\frac {x}{16}\right )}^4\,\left ({\mathrm {e}}^{1/x}\,\left (72\,x^3-24\,x^2+816\,x-816\right )+{\mathrm {e}}^{4/x}\,\left (4\,x^3-4\,x^4\right )-{\mathrm {e}}^{3/x}\,\left (72\,x^2-72\,x^3\right )+{\mathrm {e}}^{2/x}\,\left (-8\,x^4+4\,x^3-424\,x^2+424\,x\right )-136\,x^2-4\,x^4\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x/16)^3*(exp(2/x)*(848*x^2 + 8*x^4) - exp(1/x)*(3264*x + 96*x^3) - 96*x^3*exp(3/x) + 4*x^4*exp(4/x) +
272*x^2 + 4*x^4 + 4624) - log(x/16)^4*(exp(1/x)*(816*x - 24*x^2 + 72*x^3 - 816) + exp(4/x)*(4*x^3 - 4*x^4) -
exp(3/x)*(72*x^2 - 72*x^3) + exp(2/x)*(424*x - 424*x^2 + 4*x^3 - 8*x^4) - 136*x^2 - 4*x^4))/x,x)

[Out]

int((log(x/16)^3*(exp(2/x)*(848*x^2 + 8*x^4) - exp(1/x)*(3264*x + 96*x^3) - 96*x^3*exp(3/x) + 4*x^4*exp(4/x) +
272*x^2 + 4*x^4 + 4624) - log(x/16)^4*(exp(1/x)*(816*x - 24*x^2 + 72*x^3 - 816) + exp(4/x)*(4*x^3 - 4*x^4) -
exp(3/x)*(72*x^2 - 72*x^3) + exp(2/x)*(424*x - 424*x^2 + 4*x^3 - 8*x^4) - 136*x^2 - 4*x^4))/x, x)

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sympy [B]  time = 0.92, size = 105, normalized size = 3.75 \begin {gather*} x^{4} e^{\frac {4}{x}} \log {\left (\frac {x}{16} \right )}^{4} - 24 x^{3} e^{\frac {3}{x}} \log {\left (\frac {x}{16} \right )}^{4} + \left (- 24 x^{3} \log {\left (\frac {x}{16} \right )}^{4} - 816 x \log {\left (\frac {x}{16} \right )}^{4}\right ) e^{\frac {1}{x}} + \left (2 x^{4} \log {\left (\frac {x}{16} \right )}^{4} + 212 x^{2} \log {\left (\frac {x}{16} \right )}^{4}\right ) e^{\frac {2}{x}} + \left (x^{4} + 68 x^{2} + 1156\right ) \log {\left (\frac {x}{16} \right )}^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**4-4*x**3)*exp(1/x)**4+(-72*x**3+72*x**2)*exp(1/x)**3+(8*x**4-4*x**3+424*x**2-424*x)*exp(1/x)
**2+(-72*x**3+24*x**2-816*x+816)*exp(1/x)+4*x**4+136*x**2)*ln(1/16*x)**4+(4*x**4*exp(1/x)**4-96*x**3*exp(1/x)*
*3+(8*x**4+848*x**2)*exp(1/x)**2+(-96*x**3-3264*x)*exp(1/x)+4*x**4+272*x**2+4624)*ln(1/16*x)**3)/x,x)

[Out]

x**4*exp(4/x)*log(x/16)**4 - 24*x**3*exp(3/x)*log(x/16)**4 + (-24*x**3*log(x/16)**4 - 816*x*log(x/16)**4)*exp(
1/x) + (2*x**4*log(x/16)**4 + 212*x**2*log(x/16)**4)*exp(2/x) + (x**4 + 68*x**2 + 1156)*log(x/16)**4

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