3.43.32 \(\int \frac {e^2 (-2-6 x)+4 x+12 x^2+(-6 x+6 e^2 x-30 x^2) \log (4)+18 x^2 \log ^2(4)+(-8 x+8 e^2 x-40 x^2+48 x^2 \log (4)) \log (16)+32 x^2 \log ^2(16)+(2+8 x-2 e^2 x+10 x^2+(-6 x-12 x^2) \log (4)+(-8 x-16 x^2) \log (16)) \log (x)+(2 x+2 x^2) \log ^2(x)}{x} \, dx\)

Optimal. Leaf size=24 \[ \left (-e^2+\log (x)+x (2-3 \log (4)-4 \log (16)+\log (x))\right )^2 \]

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Rubi [B]  time = 0.20, antiderivative size = 160, normalized size of antiderivative = 6.67, number of steps used = 17, number of rules used = 10, integrand size = 140, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6, 14, 76, 2357, 2301, 2304, 2295, 2330, 2296, 2305} \begin {gather*} \frac {x^2}{2}+x^2 \log ^2(x)+x^2 (5-6 \log (4)-8 \log (16)) \log (x)-x^2 \log (x)+x^2 (2-4 \log (16)-\log (64)) (3-4 \log (16)-\log (64))-\frac {1}{2} x^2 (5-6 \log (4)-8 \log (16))+4 x+2 x \log ^2(x)+\log ^2(x)+2 x \left (4-e^2-\log (4194304)\right ) \log (x)-4 x \log (x)+2 x \left (2-e^2 (3-4 \log (16)-\log (64))-\log (4194304)\right )-2 x \left (4-e^2-\log (4194304)\right )-2 e^2 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^2*(-2 - 6*x) + 4*x + 12*x^2 + (-6*x + 6*E^2*x - 30*x^2)*Log[4] + 18*x^2*Log[4]^2 + (-8*x + 8*E^2*x - 40
*x^2 + 48*x^2*Log[4])*Log[16] + 32*x^2*Log[16]^2 + (2 + 8*x - 2*E^2*x + 10*x^2 + (-6*x - 12*x^2)*Log[4] + (-8*
x - 16*x^2)*Log[16])*Log[x] + (2*x + 2*x^2)*Log[x]^2)/x,x]

[Out]

4*x + x^2/2 - (x^2*(5 - 6*Log[4] - 8*Log[16]))/2 + x^2*(2 - 4*Log[16] - Log[64])*(3 - 4*Log[16] - Log[64]) - 2
*x*(4 - E^2 - Log[4194304]) + 2*x*(2 - E^2*(3 - 4*Log[16] - Log[64]) - Log[4194304]) - 2*E^2*Log[x] - 4*x*Log[
x] - x^2*Log[x] + x^2*(5 - 6*Log[4] - 8*Log[16])*Log[x] + 2*x*(4 - E^2 - Log[4194304])*Log[x] + Log[x]^2 + 2*x
*Log[x]^2 + x^2*Log[x]^2

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, 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 76

Int[((d_.)*(x_))^(n_.)*((a_) + (b_.)*(x_))*((e_) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*
x)*(d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, d, e, f, n}, x] && IGtQ[p, 0] && (NeQ[n, -1] || EqQ[p, 1]) && N
eQ[b*e + a*f, 0] && ( !IntegerQ[n] || LtQ[9*p + 5*n, 0] || GeQ[n + p + 1, 0] || (GeQ[n + p + 2, 0] && Rational
Q[a, b, d, e, f])) && (NeQ[n + p + 3, 0] || EqQ[p, 1])

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 2330

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = Expand
Integrand[(a + b*Log[c*x^n])^p, (d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n, p, q, r}
, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[r]))

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 \frac {e^2 (-2-6 x)+4 x+\left (-6 x+6 e^2 x-30 x^2\right ) \log (4)+x^2 \left (12+18 \log ^2(4)\right )+\left (-8 x+8 e^2 x-40 x^2+48 x^2 \log (4)\right ) \log (16)+32 x^2 \log ^2(16)+\left (2+8 x-2 e^2 x+10 x^2+\left (-6 x-12 x^2\right ) \log (4)+\left (-8 x-16 x^2\right ) \log (16)\right ) \log (x)+\left (2 x+2 x^2\right ) \log ^2(x)}{x} \, dx\\ &=\int \frac {e^2 (-2-6 x)+4 x+\left (-6 x+6 e^2 x-30 x^2\right ) \log (4)+\left (-8 x+8 e^2 x-40 x^2+48 x^2 \log (4)\right ) \log (16)+x^2 \left (12+18 \log ^2(4)+32 \log ^2(16)\right )+\left (2+8 x-2 e^2 x+10 x^2+\left (-6 x-12 x^2\right ) \log (4)+\left (-8 x-16 x^2\right ) \log (16)\right ) \log (x)+\left (2 x+2 x^2\right ) \log ^2(x)}{x} \, dx\\ &=\int \left (\frac {2 \left (e^2-x (2-4 \log (16)-\log (64))\right ) (-1-x (3-4 \log (16)-\log (64)))}{x}+\frac {2 \left (1+x^2 (5-6 \log (4)-8 \log (16))+x \left (4-e^2-\log (4194304)\right )\right ) \log (x)}{x}+2 (1+x) \log ^2(x)\right ) \, dx\\ &=2 \int \frac {\left (e^2-x (2-4 \log (16)-\log (64))\right ) (-1-x (3-4 \log (16)-\log (64)))}{x} \, dx+2 \int \frac {\left (1+x^2 (5-6 \log (4)-8 \log (16))+x \left (4-e^2-\log (4194304)\right )\right ) \log (x)}{x} \, dx+2 \int (1+x) \log ^2(x) \, dx\\ &=2 \int \left (2-\frac {e^2}{x}-e^2 (3-4 \log (16)-\log (64))+x (2-4 \log (16)-\log (64)) (3-4 \log (16)-\log (64))-\log (4194304)\right ) \, dx+2 \int \left (\frac {\log (x)}{x}+x (5-6 \log (4)-8 \log (16)) \log (x)+\left (4-e^2-\log (4194304)\right ) \log (x)\right ) \, dx+2 \int \left (\log ^2(x)+x \log ^2(x)\right ) \, dx\\ &=x^2 (2-4 \log (16)-\log (64)) (3-4 \log (16)-\log (64))+2 x \left (2-e^2 (3-4 \log (16)-\log (64))-\log (4194304)\right )-2 e^2 \log (x)+2 \int \frac {\log (x)}{x} \, dx+2 \int \log ^2(x) \, dx+2 \int x \log ^2(x) \, dx+(2 (5-6 \log (4)-8 \log (16))) \int x \log (x) \, dx+\left (2 \left (4-e^2-\log (4194304)\right )\right ) \int \log (x) \, dx\\ &=-\frac {1}{2} x^2 (5-6 \log (4)-8 \log (16))+x^2 (2-4 \log (16)-\log (64)) (3-4 \log (16)-\log (64))-2 x \left (4-e^2-\log (4194304)\right )+2 x \left (2-e^2 (3-4 \log (16)-\log (64))-\log (4194304)\right )-2 e^2 \log (x)+x^2 (5-6 \log (4)-8 \log (16)) \log (x)+2 x \left (4-e^2-\log (4194304)\right ) \log (x)+\log ^2(x)+2 x \log ^2(x)+x^2 \log ^2(x)-2 \int x \log (x) \, dx-4 \int \log (x) \, dx\\ &=4 x+\frac {x^2}{2}-\frac {1}{2} x^2 (5-6 \log (4)-8 \log (16))+x^2 (2-4 \log (16)-\log (64)) (3-4 \log (16)-\log (64))-2 x \left (4-e^2-\log (4194304)\right )+2 x \left (2-e^2 (3-4 \log (16)-\log (64))-\log (4194304)\right )-2 e^2 \log (x)-4 x \log (x)-x^2 \log (x)+x^2 (5-6 \log (4)-8 \log (16)) \log (x)+2 x \left (4-e^2-\log (4194304)\right ) \log (x)+\log ^2(x)+2 x \log ^2(x)+x^2 \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.16, size = 152, normalized size = 6.33 \begin {gather*} 2 \left (-2 e^2 x+2 x^2+\frac {1}{4} x^2 \log (16)+\frac {5}{4} x^2 \log (256)+2 e^2 x \log (2048)-\frac {5}{2} x^2 \log (4194304)+\frac {1}{2} x^2 \log (4) \log (4194304)+\frac {5}{2} x^2 \log (16) \log (4194304)-e^2 \log (x)+2 x \log (x)-e^2 x \log (x)+2 x^2 \log (x)-\frac {1}{2} x^2 \log (16) \log (x)-\frac {5}{2} x^2 \log (256) \log (x)-2 x \log (2048) \log (x)+\frac {\log ^2(x)}{2}+x \log ^2(x)+\frac {1}{2} x^2 \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^2*(-2 - 6*x) + 4*x + 12*x^2 + (-6*x + 6*E^2*x - 30*x^2)*Log[4] + 18*x^2*Log[4]^2 + (-8*x + 8*E^2*
x - 40*x^2 + 48*x^2*Log[4])*Log[16] + 32*x^2*Log[16]^2 + (2 + 8*x - 2*E^2*x + 10*x^2 + (-6*x - 12*x^2)*Log[4]
+ (-8*x - 16*x^2)*Log[16])*Log[x] + (2*x + 2*x^2)*Log[x]^2)/x,x]

[Out]

2*(-2*E^2*x + 2*x^2 + (x^2*Log[16])/4 + (5*x^2*Log[256])/4 + 2*E^2*x*Log[2048] - (5*x^2*Log[4194304])/2 + (x^2
*Log[4]*Log[4194304])/2 + (5*x^2*Log[16]*Log[4194304])/2 - E^2*Log[x] + 2*x*Log[x] - E^2*x*Log[x] + 2*x^2*Log[
x] - (x^2*Log[16]*Log[x])/2 - (5*x^2*Log[256]*Log[x])/2 - 2*x*Log[2048]*Log[x] + Log[x]^2/2 + x*Log[x]^2 + (x^
2*Log[x]^2)/2)

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fricas [B]  time = 1.47, size = 77, normalized size = 3.21 \begin {gather*} 484 \, x^{2} \log \relax (2)^{2} + {\left (x^{2} + 2 \, x + 1\right )} \log \relax (x)^{2} + 4 \, x^{2} - 4 \, x e^{2} - 44 \, {\left (2 \, x^{2} - x e^{2}\right )} \log \relax (2) + 2 \, {\left (2 \, x^{2} - {\left (x + 1\right )} e^{2} - 22 \, {\left (x^{2} + x\right )} \log \relax (2) + 2 \, x\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2+2*x)*log(x)^2+(4*(-16*x^2-8*x)*log(2)+2*(-12*x^2-6*x)*log(2)-2*exp(2)*x+10*x^2+8*x+2)*log(x)
+584*x^2*log(2)^2+4*(96*x^2*log(2)+8*exp(2)*x-40*x^2-8*x)*log(2)+2*(6*exp(2)*x-30*x^2-6*x)*log(2)+(-6*x-2)*exp
(2)+12*x^2+4*x)/x,x, algorithm="fricas")

[Out]

484*x^2*log(2)^2 + (x^2 + 2*x + 1)*log(x)^2 + 4*x^2 - 4*x*e^2 - 44*(2*x^2 - x*e^2)*log(2) + 2*(2*x^2 - (x + 1)
*e^2 - 22*(x^2 + x)*log(2) + 2*x)*log(x)

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giac [B]  time = 0.15, size = 94, normalized size = 3.92 \begin {gather*} 484 \, x^{2} \log \relax (2)^{2} - 44 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2} - 88 \, x^{2} \log \relax (2) + 44 \, x e^{2} \log \relax (2) + 4 \, x^{2} \log \relax (x) - 2 \, x e^{2} \log \relax (x) - 44 \, x \log \relax (2) \log \relax (x) + 2 \, x \log \relax (x)^{2} + 4 \, x^{2} - 4 \, x e^{2} + 4 \, x \log \relax (x) - 2 \, e^{2} \log \relax (x) + \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2+2*x)*log(x)^2+(4*(-16*x^2-8*x)*log(2)+2*(-12*x^2-6*x)*log(2)-2*exp(2)*x+10*x^2+8*x+2)*log(x)
+584*x^2*log(2)^2+4*(96*x^2*log(2)+8*exp(2)*x-40*x^2-8*x)*log(2)+2*(6*exp(2)*x-30*x^2-6*x)*log(2)+(-6*x-2)*exp
(2)+12*x^2+4*x)/x,x, algorithm="giac")

[Out]

484*x^2*log(2)^2 - 44*x^2*log(2)*log(x) + x^2*log(x)^2 - 88*x^2*log(2) + 44*x*e^2*log(2) + 4*x^2*log(x) - 2*x*
e^2*log(x) - 44*x*log(2)*log(x) + 2*x*log(x)^2 + 4*x^2 - 4*x*e^2 + 4*x*log(x) - 2*e^2*log(x) + log(x)^2

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maple [B]  time = 0.04, size = 82, normalized size = 3.42

method	result	size
norman	\(\ln \relax (x )^{2}+x^{2} \ln \relax (x )^{2}-2 \,{\mathrm e}^{2} \ln \relax (x )+\left (-4 \,{\mathrm e}^{2}+44 \,{\mathrm e}^{2} \ln \relax (2)\right ) x +\left (4-88 \ln \relax (2)+484 \ln \relax (2)^{2}\right ) x^{2}+\left (4-44 \ln \relax (2)\right ) x^{2} \ln \relax (x )+\left (4-2 \,{\mathrm e}^{2}-44 \ln \relax (2)\right ) x \ln \relax (x )+2 x \ln \relax (x )^{2}\)	\(82\)
risch	\(\left (x^{2}+2 x +1\right ) \ln \relax (x )^{2}+\left (-44 x^{2} \ln \relax (2)-2 \,{\mathrm e}^{2} x -44 x \ln \relax (2)+4 x^{2}+4 x \right ) \ln \relax (x )+484 x^{2} \ln \relax (2)^{2}+44 x \,{\mathrm e}^{2} \ln \relax (2)-88 x^{2} \ln \relax (2)-4 \,{\mathrm e}^{2} x +4 x^{2}-2 \,{\mathrm e}^{2} \ln \relax (x )\)	\(83\)
default	\(x^{2} \ln \relax (x )^{2}+4 x^{2} \ln \relax (x )+4 x^{2}-88 \ln \relax (2) \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )+484 x^{2} \ln \relax (2)^{2}-2 \,{\mathrm e}^{2} \left (x \ln \relax (x )-x \right )+44 x \,{\mathrm e}^{2} \ln \relax (2)+2 x \ln \relax (x )^{2}+4 x \ln \relax (x )-44 \ln \relax (2) \left (x \ln \relax (x )-x \right )-110 x^{2} \ln \relax (2)-6 \,{\mathrm e}^{2} x -44 x \ln \relax (2)-2 \,{\mathrm e}^{2} \ln \relax (x )+\ln \relax (x )^{2}\)	\(118\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2+2*x)*ln(x)^2+(4*(-16*x^2-8*x)*ln(2)+2*(-12*x^2-6*x)*ln(2)-2*exp(2)*x+10*x^2+8*x+2)*ln(x)+584*x^2*l
n(2)^2+4*(96*x^2*ln(2)+8*exp(2)*x-40*x^2-8*x)*ln(2)+2*(6*exp(2)*x-30*x^2-6*x)*ln(2)+(-6*x-2)*exp(2)+12*x^2+4*x
)/x,x,method=_RETURNVERBOSE)

[Out]

ln(x)^2+x^2*ln(x)^2-2*exp(2)*ln(x)+(-4*exp(2)+44*exp(2)*ln(2))*x+(4-88*ln(2)+484*ln(2)^2)*x^2+(4-44*ln(2))*x^2
*ln(x)+(4-2*exp(2)-44*ln(2))*x*ln(x)+2*x*ln(x)^2

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maxima [B]  time = 0.35, size = 135, normalized size = 5.62 \begin {gather*} 484 \, x^{2} \log \relax (2)^{2} + \frac {1}{2} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} - 110 \, x^{2} \log \relax (2) + 44 \, x e^{2} \log \relax (2) + 5 \, x^{2} \log \relax (x) + 2 \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x + \frac {7}{2} \, x^{2} - 2 \, {\left (x \log \relax (x) - x\right )} e^{2} - 6 \, x e^{2} - 22 \, {\left (2 \, x^{2} \log \relax (x) - x^{2}\right )} \log \relax (2) - 44 \, {\left (x \log \relax (x) - x\right )} \log \relax (2) - 44 \, x \log \relax (2) + 8 \, x \log \relax (x) - 2 \, e^{2} \log \relax (x) + \log \relax (x)^{2} - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2+2*x)*log(x)^2+(4*(-16*x^2-8*x)*log(2)+2*(-12*x^2-6*x)*log(2)-2*exp(2)*x+10*x^2+8*x+2)*log(x)
+584*x^2*log(2)^2+4*(96*x^2*log(2)+8*exp(2)*x-40*x^2-8*x)*log(2)+2*(6*exp(2)*x-30*x^2-6*x)*log(2)+(-6*x-2)*exp
(2)+12*x^2+4*x)/x,x, algorithm="maxima")

[Out]

484*x^2*log(2)^2 + 1/2*(2*log(x)^2 - 2*log(x) + 1)*x^2 - 110*x^2*log(2) + 44*x*e^2*log(2) + 5*x^2*log(x) + 2*(
log(x)^2 - 2*log(x) + 2)*x + 7/2*x^2 - 2*(x*log(x) - x)*e^2 - 6*x*e^2 - 22*(2*x^2*log(x) - x^2)*log(2) - 44*(x
*log(x) - x)*log(2) - 44*x*log(2) + 8*x*log(x) - 2*e^2*log(x) + log(x)^2 - 4*x

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mupad [B]  time = 3.03, size = 35, normalized size = 1.46 \begin {gather*} \left (2\,x+\ln \relax (x)-22\,x\,\ln \relax (2)+x\,\ln \relax (x)\right )\,\left (2\,x-2\,{\mathrm {e}}^2+\ln \relax (x)-22\,x\,\ln \relax (2)+x\,\ln \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x + 584*x^2*log(2)^2 + log(x)^2*(2*x + 2*x^2) - 4*log(2)*(8*x - 8*x*exp(2) - 96*x^2*log(2) + 40*x^2) +
log(x)*(8*x - 2*log(2)*(6*x + 12*x^2) - 4*log(2)*(8*x + 16*x^2) - 2*x*exp(2) + 10*x^2 + 2) - 2*log(2)*(6*x - 6
*x*exp(2) + 30*x^2) + 12*x^2 - exp(2)*(6*x + 2))/x,x)

[Out]

(2*x + log(x) - 22*x*log(2) + x*log(x))*(2*x - 2*exp(2) + log(x) - 22*x*log(2) + x*log(x))

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sympy [B]  time = 0.35, size = 87, normalized size = 3.62 \begin {gather*} x^{2} \left (- 88 \log {\relax (2 )} + 4 + 484 \log {\relax (2 )}^{2}\right ) + x \left (- 4 e^{2} + 44 e^{2} \log {\relax (2 )}\right ) + \left (x^{2} + 2 x + 1\right ) \log {\relax (x )}^{2} + \left (- 44 x^{2} \log {\relax (2 )} + 4 x^{2} - 44 x \log {\relax (2 )} - 2 x e^{2} + 4 x\right ) \log {\relax (x )} - 2 e^{2} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2+2*x)*ln(x)**2+(4*(-16*x**2-8*x)*ln(2)+2*(-12*x**2-6*x)*ln(2)-2*exp(2)*x+10*x**2+8*x+2)*ln(x
)+584*x**2*ln(2)**2+4*(96*x**2*ln(2)+8*exp(2)*x-40*x**2-8*x)*ln(2)+2*(6*exp(2)*x-30*x**2-6*x)*ln(2)+(-6*x-2)*e
xp(2)+12*x**2+4*x)/x,x)

[Out]

x**2*(-88*log(2) + 4 + 484*log(2)**2) + x*(-4*exp(2) + 44*exp(2)*log(2)) + (x**2 + 2*x + 1)*log(x)**2 + (-44*x
**2*log(2) + 4*x**2 - 44*x*log(2) - 2*x*exp(2) + 4*x)*log(x) - 2*exp(2)*log(x)

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