3.61.38 \(\int \frac {-614656-87808 \log (2)-4704 \log ^2(2)-112 \log ^3(2)-\log ^4(2)+(-614656-87808 \log (2)-4704 \log ^2(2)-112 \log ^3(2)-\log ^4(2)) \log (x)}{1024 x^5 \log ^5(x)} \, dx\) [6038]

Optimal. Leaf size=17 \[ \frac {(28+\log (2))^4}{4096 x^4 \log ^4(x)} \]

[Out]

1/4096/x^4*(28+ln(2))^4/ln(x)^4

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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
time = 0.38, antiderivative size = 230, normalized size of antiderivative = 13.53, number of steps used = 21, number of rules used = 7, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.113, Rules used = {12, 2343, 2346, 2209, 2413, 6874, 6617} \begin {gather*} \frac {1}{96} (28+\log (2))^4 \log (x) \text {ExpIntegralEi}(-4 \log (x))-\frac {1}{96} \left ((28+\log (2))^4 \log (x)+(28+\log (2))^4\right ) \text {ExpIntegralEi}(-4 \log (x))+\frac {1}{96} (28+\log (2))^4 \text {ExpIntegralEi}(-4 \log (x))+\frac {(28+\log (2))^4 \log (x)+(28+\log (2))^4}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4 \log (x)+(28+\log (2))^4}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}+\frac {(28+\log (2))^4 \log (x)+(28+\log (2))^4}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4}{3072 x^4 \log ^2(x)}-\frac {(28+\log (2))^4 \log (x)+(28+\log (2))^4}{384 x^4 \log (x)}+\frac {(28+\log (2))^4}{512 x^4 \log (x)}+\frac {(28+\log (2))^4}{384 x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-614656 - 87808*Log[2] - 4704*Log[2]^2 - 112*Log[2]^3 - Log[2]^4 + (-614656 - 87808*Log[2] - 4704*Log[2]^
2 - 112*Log[2]^3 - Log[2]^4)*Log[x])/(1024*x^5*Log[x]^5),x]

[Out]

(28 + Log[2])^4/(384*x^4) + (ExpIntegralEi[-4*Log[x]]*(28 + Log[2])^4)/96 + (28 + Log[2])^4/(12288*x^4*Log[x]^
3) - (28 + Log[2])^4/(3072*x^4*Log[x]^2) + (28 + Log[2])^4/(512*x^4*Log[x]) + (ExpIntegralEi[-4*Log[x]]*(28 +
Log[2])^4*Log[x])/96 - (ExpIntegralEi[-4*Log[x]]*((28 + Log[2])^4 + (28 + Log[2])^4*Log[x]))/96 + ((28 + Log[2
])^4 + (28 + Log[2])^4*Log[x])/(4096*x^4*Log[x]^4) - ((28 + Log[2])^4 + (28 + Log[2])^4*Log[x])/(3072*x^4*Log[
x]^3) + ((28 + Log[2])^4 + (28 + Log[2])^4*Log[x])/(1536*x^4*Log[x]^2) - ((28 + Log[2])^4 + (28 + Log[2])^4*Lo
g[x])/(384*x^4*Log[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 2209

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - c*(f/d)))/d)*ExpInteg
ralEi[f*g*(c + d*x)*(Log[F]/d)], x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !TrueQ[$UseGamma]

Rule 2343

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

Rule 2346

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))^(p_)*(x_)^(m_.), x_Symbol] :> Dist[1/c^(m + 1), Subst[Int[E^((m + 1)*x)*(a
+ b*x)^p, x], x, Log[c*x]], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[m]

Rule 2413

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.) + Log[(f_.)*(x_)^(r_.)]*(e_.))*((g_.)*(x_))^(m_.), x_Sy
mbol] :> With[{u = IntHide[(g*x)^m*(a + b*Log[c*x^n])^p, x]}, Dist[d + e*Log[f*x^r], u, x] - Dist[e*r, Int[Sim
plifyIntegrand[u/x, x], x], x]] /; FreeQ[{a, b, c, d, e, f, g, m, n, p, r}, x] &&  !(EqQ[p, 1] && EqQ[a, 0] &&
NeQ[d, 0])

Rule 6617

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

Rule 6874

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-614656-87808 \log (2)-4704 \log ^2(2)-112 \log ^3(2)-\log ^4(2)+\left (-614656-87808 \log (2)-4704 \log ^2(2)-112 \log ^3(2)-\log ^4(2)\right ) \log (x)}{x^5 \log ^5(x)} \, dx}{1024}\\ &=-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {(28+\log (2))^4 \int \frac {-3+4 \log (x)-8 \log ^2(x)+32 \log ^3(x)+128 x^4 \text {Ei}(-4 \log (x)) \log ^4(x)}{12 x^5 \log ^4(x)} \, dx}{1024}\\ &=-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {(28+\log (2))^4 \int \frac {-3+4 \log (x)-8 \log ^2(x)+32 \log ^3(x)+128 x^4 \text {Ei}(-4 \log (x)) \log ^4(x)}{x^5 \log ^4(x)} \, dx}{12288}\\ &=-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {(28+\log (2))^4 \int \left (\frac {128 \text {Ei}(-4 \log (x))}{x}-\frac {3}{x^5 \log ^4(x)}+\frac {4}{x^5 \log ^3(x)}-\frac {8}{x^5 \log ^2(x)}+\frac {32}{x^5 \log (x)}\right ) \, dx}{12288}\\ &=-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}-\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^4(x)} \, dx}{4096}+\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^3(x)} \, dx}{3072}-\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^2(x)} \, dx}{1536}+\frac {1}{384} (28+\log (2))^4 \int \frac {1}{x^5 \log (x)} \, dx+\frac {1}{96} (28+\log (2))^4 \int \frac {\text {Ei}(-4 \log (x))}{x} \, dx\\ &=\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}-\frac {(28+\log (2))^4}{6144 x^4 \log ^2(x)}+\frac {(28+\log (2))^4}{1536 x^4 \log (x)}-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^3(x)} \, dx}{3072}-\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^2(x)} \, dx}{1536}+\frac {1}{384} (28+\log (2))^4 \int \frac {1}{x^5 \log (x)} \, dx+\frac {1}{384} (28+\log (2))^4 \text {Subst}\left (\int \frac {e^{-4 x}}{x} \, dx,x,\log (x)\right )+\frac {1}{96} (28+\log (2))^4 \text {Subst}(\int \text {Ei}(-4 x) \, dx,x,\log (x))\\ &=\frac {(28+\log (2))^4}{384 x^4}+\frac {1}{384} \text {Ei}(-4 \log (x)) (28+\log (2))^4+\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}-\frac {(28+\log (2))^4}{3072 x^4 \log ^2(x)}+\frac {(28+\log (2))^4}{768 x^4 \log (x)}+\frac {1}{96} \text {Ei}(-4 \log (x)) (28+\log (2))^4 \log (x)-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}-\frac {(28+\log (2))^4 \int \frac {1}{x^5 \log ^2(x)} \, dx}{1536}+\frac {1}{384} (28+\log (2))^4 \int \frac {1}{x^5 \log (x)} \, dx+\frac {1}{384} (28+\log (2))^4 \text {Subst}\left (\int \frac {e^{-4 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {(28+\log (2))^4}{384 x^4}+\frac {1}{192} \text {Ei}(-4 \log (x)) (28+\log (2))^4+\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}-\frac {(28+\log (2))^4}{3072 x^4 \log ^2(x)}+\frac {(28+\log (2))^4}{512 x^4 \log (x)}+\frac {1}{96} \text {Ei}(-4 \log (x)) (28+\log (2))^4 \log (x)-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {1}{384} (28+\log (2))^4 \int \frac {1}{x^5 \log (x)} \, dx+\frac {1}{384} (28+\log (2))^4 \text {Subst}\left (\int \frac {e^{-4 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {(28+\log (2))^4}{384 x^4}+\frac {1}{128} \text {Ei}(-4 \log (x)) (28+\log (2))^4+\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}-\frac {(28+\log (2))^4}{3072 x^4 \log ^2(x)}+\frac {(28+\log (2))^4}{512 x^4 \log (x)}+\frac {1}{96} \text {Ei}(-4 \log (x)) (28+\log (2))^4 \log (x)-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}+\frac {1}{384} (28+\log (2))^4 \text {Subst}\left (\int \frac {e^{-4 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {(28+\log (2))^4}{384 x^4}+\frac {1}{96} \text {Ei}(-4 \log (x)) (28+\log (2))^4+\frac {(28+\log (2))^4}{12288 x^4 \log ^3(x)}-\frac {(28+\log (2))^4}{3072 x^4 \log ^2(x)}+\frac {(28+\log (2))^4}{512 x^4 \log (x)}+\frac {1}{96} \text {Ei}(-4 \log (x)) (28+\log (2))^4 \log (x)-\frac {1}{96} \text {Ei}(-4 \log (x)) \left ((28+\log (2))^4+(28+\log (2))^4 \log (x)\right )+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{4096 x^4 \log ^4(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{3072 x^4 \log ^3(x)}+\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{1536 x^4 \log ^2(x)}-\frac {(28+\log (2))^4+(28+\log (2))^4 \log (x)}{384 x^4 \log (x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {(28+\log (2))^4}{4096 x^4 \log ^4(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-614656 - 87808*Log[2] - 4704*Log[2]^2 - 112*Log[2]^3 - Log[2]^4 + (-614656 - 87808*Log[2] - 4704*L
og[2]^2 - 112*Log[2]^3 - Log[2]^4)*Log[x])/(1024*x^5*Log[x]^5),x]

[Out]

(28 + Log[2])^4/(4096*x^4*Log[x]^4)

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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.10, size = 379, normalized size = 22.29

method	result	size
risch	\(\frac {\ln \left (2\right )^{4}+112 \ln \left (2\right )^{3}+4704 \ln \left (2\right )^{2}+87808 \ln \left (2\right )+614656}{4096 x^{4} \ln \left (x \right )^{4}}\)	\(32\)
default	\(-\frac {\ln \left (2\right )^{4} \left (-\frac {1}{3 x^{4} \ln \left (x \right )^{3}}+\frac {2}{3 x^{4} \ln \left (x \right )^{2}}-\frac {8}{3 x^{4} \ln \left (x \right )}+\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{1024}-\frac {7 \ln \left (2\right )^{3} \left (-\frac {1}{3 x^{4} \ln \left (x \right )^{3}}+\frac {2}{3 x^{4} \ln \left (x \right )^{2}}-\frac {8}{3 x^{4} \ln \left (x \right )}+\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{64}-\frac {\ln \left (2\right )^{4} \left (-\frac {1}{4 x^{4} \ln \left (x \right )^{4}}+\frac {1}{3 x^{4} \ln \left (x \right )^{3}}-\frac {2}{3 x^{4} \ln \left (x \right )^{2}}+\frac {8}{3 x^{4} \ln \left (x \right )}-\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{1024}-\frac {147 \ln \left (2\right )^{2} \left (-\frac {1}{3 x^{4} \ln \left (x \right )^{3}}+\frac {2}{3 x^{4} \ln \left (x \right )^{2}}-\frac {8}{3 x^{4} \ln \left (x \right )}+\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{32}-\frac {7 \ln \left (2\right )^{3} \left (-\frac {1}{4 x^{4} \ln \left (x \right )^{4}}+\frac {1}{3 x^{4} \ln \left (x \right )^{3}}-\frac {2}{3 x^{4} \ln \left (x \right )^{2}}+\frac {8}{3 x^{4} \ln \left (x \right )}-\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{64}-\frac {343 \ln \left (2\right ) \left (-\frac {1}{3 x^{4} \ln \left (x \right )^{3}}+\frac {2}{3 x^{4} \ln \left (x \right )^{2}}-\frac {8}{3 x^{4} \ln \left (x \right )}+\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{4}-\frac {147 \ln \left (2\right )^{2} \left (-\frac {1}{4 x^{4} \ln \left (x \right )^{4}}+\frac {1}{3 x^{4} \ln \left (x \right )^{3}}-\frac {2}{3 x^{4} \ln \left (x \right )^{2}}+\frac {8}{3 x^{4} \ln \left (x \right )}-\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{32}-\frac {343 \ln \left (2\right ) \left (-\frac {1}{4 x^{4} \ln \left (x \right )^{4}}+\frac {1}{3 x^{4} \ln \left (x \right )^{3}}-\frac {2}{3 x^{4} \ln \left (x \right )^{2}}+\frac {8}{3 x^{4} \ln \left (x \right )}-\frac {32 \expIntegral \left (1, 4 \ln \left (x \right )\right )}{3}\right )}{4}+\frac {2401}{16 x^{4} \ln \left (x \right )^{4}}\)	\(379\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/1024*((-ln(2)^4-112*ln(2)^3-4704*ln(2)^2-87808*ln(2)-614656)*ln(x)-ln(2)^4-112*ln(2)^3-4704*ln(2)^2-8780
8*ln(2)-614656)/x^5/ln(x)^5,x,method=_RETURNVERBOSE)

[Out]

-1/1024*ln(2)^4*(-1/3/x^4/ln(x)^3+2/3/x^4/ln(x)^2-8/3/x^4/ln(x)+32/3*Ei(1,4*ln(x)))-7/64*ln(2)^3*(-1/3/x^4/ln(
x)^3+2/3/x^4/ln(x)^2-8/3/x^4/ln(x)+32/3*Ei(1,4*ln(x)))-1/1024*ln(2)^4*(-1/4/x^4/ln(x)^4+1/3/x^4/ln(x)^3-2/3/x^
4/ln(x)^2+8/3/x^4/ln(x)-32/3*Ei(1,4*ln(x)))-147/32*ln(2)^2*(-1/3/x^4/ln(x)^3+2/3/x^4/ln(x)^2-8/3/x^4/ln(x)+32/
3*Ei(1,4*ln(x)))-7/64*ln(2)^3*(-1/4/x^4/ln(x)^4+1/3/x^4/ln(x)^3-2/3/x^4/ln(x)^2+8/3/x^4/ln(x)-32/3*Ei(1,4*ln(x
)))-343/4*ln(2)*(-1/3/x^4/ln(x)^3+2/3/x^4/ln(x)^2-8/3/x^4/ln(x)+32/3*Ei(1,4*ln(x)))-147/32*ln(2)^2*(-1/4/x^4/l
n(x)^4+1/3/x^4/ln(x)^3-2/3/x^4/ln(x)^2+8/3/x^4/ln(x)-32/3*Ei(1,4*ln(x)))-343/4*ln(2)*(-1/4/x^4/ln(x)^4+1/3/x^4
/ln(x)^3-2/3/x^4/ln(x)^2+8/3/x^4/ln(x)-32/3*Ei(1,4*ln(x)))+2401/16/x^4/ln(x)^4

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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.33, size = 109, normalized size = 6.41 \begin {gather*} \frac {1}{16} \, \Gamma \left (-3, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{4} + \frac {1}{4} \, \Gamma \left (-4, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{4} + 7 \, \Gamma \left (-3, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{3} + 28 \, \Gamma \left (-4, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{3} + 294 \, \Gamma \left (-3, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{2} + 1176 \, \Gamma \left (-4, 4 \, \log \left (x\right )\right ) \log \left (2\right )^{2} + 5488 \, \Gamma \left (-3, 4 \, \log \left (x\right )\right ) \log \left (2\right ) + 21952 \, \Gamma \left (-4, 4 \, \log \left (x\right )\right ) \log \left (2\right ) + 38416 \, \Gamma \left (-3, 4 \, \log \left (x\right )\right ) + 153664 \, \Gamma \left (-4, 4 \, \log \left (x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/1024*((-log(2)^4-112*log(2)^3-4704*log(2)^2-87808*log(2)-614656)*log(x)-log(2)^4-112*log(2)^3-4704
*log(2)^2-87808*log(2)-614656)/x^5/log(x)^5,x, algorithm="maxima")

[Out]

1/16*gamma(-3, 4*log(x))*log(2)^4 + 1/4*gamma(-4, 4*log(x))*log(2)^4 + 7*gamma(-3, 4*log(x))*log(2)^3 + 28*gam
ma(-4, 4*log(x))*log(2)^3 + 294*gamma(-3, 4*log(x))*log(2)^2 + 1176*gamma(-4, 4*log(x))*log(2)^2 + 5488*gamma(
-3, 4*log(x))*log(2) + 21952*gamma(-4, 4*log(x))*log(2) + 38416*gamma(-3, 4*log(x)) + 153664*gamma(-4, 4*log(x
))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (15) = 30\).
time = 0.36, size = 31, normalized size = 1.82 \begin {gather*} \frac {\log \left (2\right )^{4} + 112 \, \log \left (2\right )^{3} + 4704 \, \log \left (2\right )^{2} + 87808 \, \log \left (2\right ) + 614656}{4096 \, x^{4} \log \left (x\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/1024*((-log(2)^4-112*log(2)^3-4704*log(2)^2-87808*log(2)-614656)*log(x)-log(2)^4-112*log(2)^3-4704
*log(2)^2-87808*log(2)-614656)/x^5/log(x)^5,x, algorithm="fricas")

[Out]

1/4096*(log(2)^4 + 112*log(2)^3 + 4704*log(2)^2 + 87808*log(2) + 614656)/(x^4*log(x)^4)

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 34 vs. \(2 (15) = 30\).
time = 0.05, size = 34, normalized size = 2.00 \begin {gather*} \frac {\log {\left (2 \right )}^{4} + 112 \log {\left (2 \right )}^{3} + 4704 \log {\left (2 \right )}^{2} + 87808 \log {\left (2 \right )} + 614656}{4096 x^{4} \log {\left (x \right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/1024*((-ln(2)**4-112*ln(2)**3-4704*ln(2)**2-87808*ln(2)-614656)*ln(x)-ln(2)**4-112*ln(2)**3-4704*l
n(2)**2-87808*ln(2)-614656)/x**5/ln(x)**5,x)

[Out]

(log(2)**4 + 112*log(2)**3 + 4704*log(2)**2 + 87808*log(2) + 614656)/(4096*x**4*log(x)**4)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (15) = 30\).
time = 0.39, size = 31, normalized size = 1.82 \begin {gather*} \frac {\log \left (2\right )^{4} + 112 \, \log \left (2\right )^{3} + 4704 \, \log \left (2\right )^{2} + 87808 \, \log \left (2\right ) + 614656}{4096 \, x^{4} \log \left (x\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/1024*((-log(2)^4-112*log(2)^3-4704*log(2)^2-87808*log(2)-614656)*log(x)-log(2)^4-112*log(2)^3-4704
*log(2)^2-87808*log(2)-614656)/x^5/log(x)^5,x, algorithm="giac")

[Out]

1/4096*(log(2)^4 + 112*log(2)^3 + 4704*log(2)^2 + 87808*log(2) + 614656)/(x^4*log(x)^4)

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Mupad [B]
time = 4.34, size = 15, normalized size = 0.88 \begin {gather*} \frac {{\left (\ln \left (2\right )+28\right )}^4}{4096\,x^4\,{\ln \left (x\right )}^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((343*log(2))/4 + (log(x)*(87808*log(2) + 4704*log(2)^2 + 112*log(2)^3 + log(2)^4 + 614656))/1024 + (147*
log(2)^2)/32 + (7*log(2)^3)/64 + log(2)^4/1024 + 2401/4)/(x^5*log(x)^5),x)

[Out]

(log(2) + 28)^4/(4096*x^4*log(x)^4)

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