3.2.97 \(\int \frac {108+54 x-2 x^3+e^x (-60+22 x-2 x^2)+(-12+2 x) \log (-6+x)+(37 x+6 x^2-2 x^3+e^x (-24 x+10 x^2-x^3)) \log (x^2)}{-6 x+x^2} \, dx\)

Optimal. Leaf size=27 \[ 5-\left (e^x (-5+x)+(3+x)^2-\log (-6+x)\right ) \log \left (x^2\right ) \]

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Rubi [C]  time = 1.14, antiderivative size = 87, normalized size of antiderivative = 3.22, number of steps used = 35, number of rules used = 19, integrand size = 81, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.235, Rules used = {1593, 6742, 36, 31, 29, 43, 2394, 2315, 2317, 2391, 2351, 2295, 2304, 2199, 2194, 2178, 2176, 2554, 12} \begin {gather*} 2 \text {Li}_2\left (1-\frac {x}{6}\right )+2 \text {Li}_2\left (\frac {x}{6}\right )+x^2 \left (-\log \left (x^2\right )\right )-6 x \log \left (x^2\right )+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \log (x-6) \log \left (\frac {x}{6}\right )-18 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(108 + 54*x - 2*x^3 + E^x*(-60 + 22*x - 2*x^2) + (-12 + 2*x)*Log[-6 + x] + (37*x + 6*x^2 - 2*x^3 + E^x*(-2
4*x + 10*x^2 - x^3))*Log[x^2])/(-6*x + x^2),x]

[Out]

2*Log[-6 + x]*Log[x/6] - 18*Log[x] + E^x*Log[x^2] + E^x*(4 - x)*Log[x^2] - 6*x*Log[x^2] - x^2*Log[x^2] + Log[1
- x/6]*Log[x^2] + 2*PolyLog[2, 1 - x/6] + 2*PolyLog[2, x/6]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 36

Int[1/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Dist[b/(b*c - a*d), Int[1/(a + b*x), x], x] -
Dist[d/(b*c - a*d), Int[1/(c + d*x), x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 1593

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

Rule 2178

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

Rule 2194

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

Rule 2199

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), w*NormalizePo
werOfLinear[u, x]^m, x], x] /; FreeQ[{F, c}, x] && PolynomialQ[w, x] && LinearQ[v, x] && PowerOfLinearQ[u, x]
&& IntegerQ[m] &&  !$UseGamma === True

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 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 2315

Int[Log[(c_.)*(x_)]/((d_) + (e_.)*(x_)), x_Symbol] :> -Simp[PolyLog[2, 1 - c*x]/e, x] /; FreeQ[{c, d, e}, x] &
& EqQ[e + c*d, 0]

Rule 2317

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[(Log[1 + (e*x)/d]*(a +
b*Log[c*x^n])^p)/e, x] - Dist[(b*n*p)/e, Int[(Log[1 + (e*x)/d]*(a + b*Log[c*x^n])^(p - 1))/x, x], x] /; FreeQ[
{a, b, c, d, e, n}, x] && IGtQ[p, 0]

Rule 2351

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((f_.)*(x_))^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> Wit
h[{u = ExpandIntegrand[a + b*Log[c*x^n], (f*x)^m*(d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c,
d, e, f, m, n, q, r}, x] && IntegerQ[q] && (GtQ[q, 0] || (IntegerQ[m] && IntegerQ[r]))

Rule 2391

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> -Simp[PolyLog[2, -(c*e*x^n)]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

Rule 2394

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))/((f_.) + (g_.)*(x_)), x_Symbol] :> Simp[(Log[(e*(f +
g*x))/(e*f - d*g)]*(a + b*Log[c*(d + e*x)^n]))/g, x] - Dist[(b*e*n)/g, Int[Log[(e*(f + g*x))/(e*f - d*g)]/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n}, x] && NeQ[e*f - d*g, 0]

Rule 2554

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[(w*D[u, x]
)/u, x], x] /; InverseFunctionFreeQ[w, x]] /; InverseFunctionFreeQ[u, x]

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 \frac {108+54 x-2 x^3+e^x \left (-60+22 x-2 x^2\right )+(-12+2 x) \log (-6+x)+\left (37 x+6 x^2-2 x^3+e^x \left (-24 x+10 x^2-x^3\right )\right ) \log \left (x^2\right )}{(-6+x) x} \, dx\\ &=\int \left (\frac {54}{-6+x}+\frac {108}{(-6+x) x}-\frac {2 x^2}{-6+x}+\frac {2 \log (-6+x)}{x}+\frac {37 \log \left (x^2\right )}{-6+x}+\frac {6 x \log \left (x^2\right )}{-6+x}-\frac {2 x^2 \log \left (x^2\right )}{-6+x}-\frac {e^x \left (-10+2 x-4 x \log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x}\right ) \, dx\\ &=54 \log (6-x)-2 \int \frac {x^2}{-6+x} \, dx+2 \int \frac {\log (-6+x)}{x} \, dx-2 \int \frac {x^2 \log \left (x^2\right )}{-6+x} \, dx+6 \int \frac {x \log \left (x^2\right )}{-6+x} \, dx+37 \int \frac {\log \left (x^2\right )}{-6+x} \, dx+108 \int \frac {1}{(-6+x) x} \, dx-\int \frac {e^x \left (-10+2 x-4 x \log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x} \, dx\\ &=54 \log (6-x)+2 \log (-6+x) \log \left (\frac {x}{6}\right )+37 \log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )-2 \int \left (6+\frac {36}{-6+x}+x\right ) \, dx-2 \int \frac {\log \left (\frac {x}{6}\right )}{-6+x} \, dx-2 \int \left (6 \log \left (x^2\right )+\frac {36 \log \left (x^2\right )}{-6+x}+x \log \left (x^2\right )\right ) \, dx+6 \int \left (\log \left (x^2\right )+\frac {6 \log \left (x^2\right )}{-6+x}\right ) \, dx+18 \int \frac {1}{-6+x} \, dx-18 \int \frac {1}{x} \, dx-74 \int \frac {\log \left (1-\frac {x}{6}\right )}{x} \, dx-\int \left (\frac {2 e^x (-5+x)}{x}+e^x (-4+x) \log \left (x^2\right )\right ) \, dx\\ &=-12 x-x^2+2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+37 \log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+74 \text {Li}_2\left (\frac {x}{6}\right )-2 \int \frac {e^x (-5+x)}{x} \, dx-2 \int x \log \left (x^2\right ) \, dx+6 \int \log \left (x^2\right ) \, dx-12 \int \log \left (x^2\right ) \, dx+36 \int \frac {\log \left (x^2\right )}{-6+x} \, dx-72 \int \frac {\log \left (x^2\right )}{-6+x} \, dx-\int e^x (-4+x) \log \left (x^2\right ) \, dx\\ &=2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )-6 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+74 \text {Li}_2\left (\frac {x}{6}\right )-2 \int \left (e^x-\frac {5 e^x}{x}\right ) \, dx-72 \int \frac {\log \left (1-\frac {x}{6}\right )}{x} \, dx+144 \int \frac {\log \left (1-\frac {x}{6}\right )}{x} \, dx+\int \frac {2 e^x (-5+x)}{x} \, dx\\ &=2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )-6 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+2 \text {Li}_2\left (\frac {x}{6}\right )-2 \int e^x \, dx+2 \int \frac {e^x (-5+x)}{x} \, dx+10 \int \frac {e^x}{x} \, dx\\ &=-2 e^x+10 \text {Ei}(x)+2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )-6 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+2 \text {Li}_2\left (\frac {x}{6}\right )+2 \int \left (e^x-\frac {5 e^x}{x}\right ) \, dx\\ &=-2 e^x+10 \text {Ei}(x)+2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )-6 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+2 \text {Li}_2\left (\frac {x}{6}\right )+2 \int e^x \, dx-10 \int \frac {e^x}{x} \, dx\\ &=2 \log (-6+x) \log \left (\frac {x}{6}\right )-18 \log (x)+e^x \log \left (x^2\right )+e^x (4-x) \log \left (x^2\right )-6 x \log \left (x^2\right )-x^2 \log \left (x^2\right )+\log \left (1-\frac {x}{6}\right ) \log \left (x^2\right )+2 \text {Li}_2\left (1-\frac {x}{6}\right )+2 \text {Li}_2\left (\frac {x}{6}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.39, size = 30, normalized size = 1.11 \begin {gather*} -18 \log (x)-\left (e^x (-5+x)+x (6+x)-\log (-6+x)\right ) \log \left (x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(108 + 54*x - 2*x^3 + E^x*(-60 + 22*x - 2*x^2) + (-12 + 2*x)*Log[-6 + x] + (37*x + 6*x^2 - 2*x^3 + E
^x*(-24*x + 10*x^2 - x^3))*Log[x^2])/(-6*x + x^2),x]

[Out]

-18*Log[x] - (E^x*(-5 + x) + x*(6 + x) - Log[-6 + x])*Log[x^2]

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fricas [A]  time = 1.38, size = 26, normalized size = 0.96 \begin {gather*} -{\left (x^{2} + {\left (x - 5\right )} e^{x} + 6 \, x - \log \left (x - 6\right ) + 9\right )} \log \left (x^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3+10*x^2-24*x)*exp(x)-2*x^3+6*x^2+37*x)*log(x^2)+(2*x-12)*log(x-6)+(-2*x^2+22*x-60)*exp(x)-2*x
^3+54*x+108)/(x^2-6*x),x, algorithm="fricas")

[Out]

-(x^2 + (x - 5)*e^x + 6*x - log(x - 6) + 9)*log(x^2)

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giac [A]  time = 0.35, size = 42, normalized size = 1.56 \begin {gather*} -x e^{x} \log \left (x^{2}\right ) - 2 \, x^{2} \log \relax (x) + 5 \, e^{x} \log \left (x^{2}\right ) - 12 \, x \log \relax (x) + 2 \, \log \left (x - 6\right ) \log \relax (x) - 18 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3+10*x^2-24*x)*exp(x)-2*x^3+6*x^2+37*x)*log(x^2)+(2*x-12)*log(x-6)+(-2*x^2+22*x-60)*exp(x)-2*x
^3+54*x+108)/(x^2-6*x),x, algorithm="giac")

[Out]

-x*e^x*log(x^2) - 2*x^2*log(x) + 5*e^x*log(x^2) - 12*x*log(x) + 2*log(x - 6)*log(x) - 18*log(x)

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maple [B]  time = 0.18, size = 71, normalized size = 2.63

method	result	size
default	\(5 \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right ) {\mathrm e}^{x}+10 \,{\mathrm e}^{x} \ln \relax (x )-x \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right ) {\mathrm e}^{x}-2 x \,{\mathrm e}^{x} \ln \relax (x )-18 \ln \relax (x )-6 x \ln \left (x^{2}\right )-x^{2} \ln \left (x^{2}\right )+\ln \left (x -6\right ) \ln \left (x^{2}\right )\)	\(71\)
risch	\(2 \ln \relax (x ) \ln \left (x -6\right )-2 x^{2} \ln \relax (x )-2 x \,{\mathrm e}^{x} \ln \relax (x )-12 x \ln \relax (x )+10 \,{\mathrm e}^{x} \ln \relax (x )-\frac {i \pi \ln \left (\left (-\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-36 i\right ) x +6 \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-12 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+6 \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+216 i\right ) \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-\frac {i \pi \ln \left (\left (-\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-36 i\right ) x +6 \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-12 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+6 \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+216 i\right ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {5 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}}{2}+5 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}-i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-6 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {5 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}}{2}+\frac {i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}}{2}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-18 \ln \left (-x \right )+3 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+3 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}+i \pi \ln \left (\left (-\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-36 i\right ) x +6 \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-12 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+6 \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+216 i\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}+\frac {i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}}{2}\)	\(616\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^3+10*x^2-24*x)*exp(x)-2*x^3+6*x^2+37*x)*ln(x^2)+(2*x-12)*ln(x-6)+(-2*x^2+22*x-60)*exp(x)-2*x^3+54*x+
108)/(x^2-6*x),x,method=_RETURNVERBOSE)

[Out]

5*(ln(x^2)-2*ln(x))*exp(x)+10*exp(x)*ln(x)-x*(ln(x^2)-2*ln(x))*exp(x)-2*x*exp(x)*ln(x)-18*ln(x)-6*x*ln(x^2)-x^
2*ln(x^2)+ln(x-6)*ln(x^2)

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maxima [A]  time = 0.80, size = 41, normalized size = 1.52 \begin {gather*} -2 \, {\left (x - 5\right )} e^{x} \log \relax (x) + 2 \, {\left (\log \relax (x) - 9\right )} \log \left (x - 6\right ) - 2 \, {\left (x^{2} + 6 \, x\right )} \log \relax (x) + 18 \, \log \left (x - 6\right ) - 18 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^3+10*x^2-24*x)*exp(x)-2*x^3+6*x^2+37*x)*log(x^2)+(2*x-12)*log(x-6)+(-2*x^2+22*x-60)*exp(x)-2*x
^3+54*x+108)/(x^2-6*x),x, algorithm="maxima")

[Out]

-2*(x - 5)*e^x*log(x) + 2*(log(x) - 9)*log(x - 6) - 2*(x^2 + 6*x)*log(x) + 18*log(x - 6) - 18*log(x)

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mupad [B]  time = 0.59, size = 59, normalized size = 2.19 \begin {gather*} \ln \left (x^2\right )\,\left (\ln \left (x-6\right )+\frac {36\,x^2-x^4}{x\,\left (x-6\right )}-\frac {{\mathrm {e}}^x\,\left (x^3-11\,x^2+30\,x\right )}{x\,\left (x-6\right )}\right )-18\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(54*x - exp(x)*(2*x^2 - 22*x + 60) + log(x^2)*(37*x - exp(x)*(24*x - 10*x^2 + x^3) + 6*x^2 - 2*x^3) - 2*x
^3 + log(x - 6)*(2*x - 12) + 108)/(6*x - x^2),x)

[Out]

log(x^2)*(log(x - 6) + (36*x^2 - x^4)/(x*(x - 6)) - (exp(x)*(30*x - 11*x^2 + x^3))/(x*(x - 6))) - 18*log(x)

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sympy [A]  time = 0.60, size = 44, normalized size = 1.63 \begin {gather*} \left (- x^{2} - 6 x\right ) \log {\left (x^{2} \right )} + \left (- x \log {\left (x^{2} \right )} + 5 \log {\left (x^{2} \right )}\right ) e^{x} - 18 \log {\relax (x )} + \log {\left (x^{2} \right )} \log {\left (x - 6 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**3+10*x**2-24*x)*exp(x)-2*x**3+6*x**2+37*x)*ln(x**2)+(2*x-12)*ln(x-6)+(-2*x**2+22*x-60)*exp(x)
-2*x**3+54*x+108)/(x**2-6*x),x)

[Out]

(-x**2 - 6*x)*log(x**2) + (-x*log(x**2) + 5*log(x**2))*exp(x) - 18*log(x) + log(x**2)*log(x - 6)

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