\(\int \frac {(25-5 x-5 e^{\frac {x}{\log (3)}} x)^2 ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} (2 x^2+3 x \log (3)))}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx\) [7518]

Optimal result

Integrand size = 69, antiderivative size = 21 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 x \left (5-x-e^{\frac {x}{\log (3)}} x\right )^2 \]

[Out]

(-5*x*exp(x/ln(3))-5*x+25)^2*x

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(278\) vs. \(2(21)=42\).

Time = 0.53 (sec) , antiderivative size = 278, normalized size of antiderivative = 13.24, number of steps used = 25, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {6820, 12, 6874, 2227, 2207, 2225} \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 x^3+50 x^3 e^{\frac {x}{\log (3)}}+25 x^3 e^{\frac {2 x}{\log (3)}}-250 x^2+\frac {25}{2} x^2 \log (27) e^{\frac {2 x}{\log (3)}}-50 x^2 (5-\log (27)) e^{\frac {x}{\log (3)}}-150 x^2 \log (3) e^{\frac {x}{\log (3)}}-\frac {75}{2} x^2 \log (3) e^{\frac {2 x}{\log (3)}}+625 x-300 \log ^3(3) e^{\frac {x}{\log (3)}}-\frac {75}{4} \log ^3(3) e^{\frac {2 x}{\log (3)}}+300 x \log ^2(3) e^{\frac {x}{\log (3)}}+\frac {75}{2} x \log ^2(3) e^{\frac {2 x}{\log (3)}}+\frac {25}{4} \log ^2(3) \log (27) e^{\frac {2 x}{\log (3)}}-100 \log ^2(3) (5-\log (27)) e^{\frac {x}{\log (3)}}-125 x \log (81) e^{\frac {x}{\log (3)}}-\frac {25}{2} x \log (3) \log (27) e^{\frac {2 x}{\log (3)}}+100 x \log (3) (5-\log (27)) e^{\frac {x}{\log (3)}}+125 \log (3) \log (81) e^{\frac {x}{\log (3)}} \]

[In]

Int[((25 - 5*x - 5*E^(x/Log[3])*x)^2*((-5 + 3*x)*Log[3] + E^(x/Log[3])*(2*x^2 + 3*x*Log[3])))/((-5 + x)*Log[3]
+ E^(x/Log[3])*x*Log[3]),x]

[Out]

625*x - 250*x^2 + 25*x^3 + 50*E^(x/Log[3])*x^3 + 25*E^((2*x)/Log[3])*x^3 - 150*E^(x/Log[3])*x^2*Log[3] - (75*E
^((2*x)/Log[3])*x^2*Log[3])/2 + 300*E^(x/Log[3])*x*Log[3]^2 + (75*E^((2*x)/Log[3])*x*Log[3]^2)/2 - 300*E^(x/Lo
g[3])*Log[3]^3 - (75*E^((2*x)/Log[3])*Log[3]^3)/4 - 50*E^(x/Log[3])*x^2*(5 - Log[27]) + 100*E^(x/Log[3])*x*Log
[3]*(5 - Log[27]) - 100*E^(x/Log[3])*Log[3]^2*(5 - Log[27]) + (25*E^((2*x)/Log[3])*x^2*Log[27])/2 - (25*E^((2*
x)/Log[3])*x*Log[3]*Log[27])/2 + (25*E^((2*x)/Log[3])*Log[3]^2*Log[27])/4 - 125*E^(x/Log[3])*x*Log[81] + 125*E
^(x/Log[3])*Log[3]*Log[81]

Rule 12

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

Rule 2207

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] &&  !TrueQ[$UseGamma]

Rule 2225

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 2227

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !TrueQ[$UseGamma]

Rule 6820

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

Rule 6874

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {25 \left (5-x-e^{\frac {x}{\log (3)}} x\right ) \left (-((-5+3 x) \log (3))-e^{\frac {x}{\log (3)}} x (2 x+\log (27))\right )}{\log (3)} \, dx \\ & = \frac {25 \int \left (5-x-e^{\frac {x}{\log (3)}} x\right ) \left (-((-5+3 x) \log (3))-e^{\frac {x}{\log (3)}} x (2 x+\log (27))\right ) \, dx}{\log (3)} \\ & = \frac {25 \int \left (\left (25-20 x+3 x^2\right ) \log (3)+e^{\frac {2 x}{\log (3)}} x^2 (2 x+\log (27))+e^{\frac {x}{\log (3)}} x \left (2 x^2-2 x (5-\log (27))-5 \log (81)\right )\right ) \, dx}{\log (3)} \\ & = 25 \int \left (25-20 x+3 x^2\right ) \, dx+\frac {25 \int e^{\frac {2 x}{\log (3)}} x^2 (2 x+\log (27)) \, dx}{\log (3)}+\frac {25 \int e^{\frac {x}{\log (3)}} x \left (2 x^2-2 x (5-\log (27))-5 \log (81)\right ) \, dx}{\log (3)} \\ & = 625 x-250 x^2+25 x^3+\frac {25 \int \left (2 e^{\frac {2 x}{\log (3)}} x^3+e^{\frac {2 x}{\log (3)}} x^2 \log (27)\right ) \, dx}{\log (3)}+\frac {25 \int \left (2 e^{\frac {x}{\log (3)}} x^3+2 e^{\frac {x}{\log (3)}} x^2 (-5+\log (27))-5 e^{\frac {x}{\log (3)}} x \log (81)\right ) \, dx}{\log (3)} \\ & = 625 x-250 x^2+25 x^3+\frac {50 \int e^{\frac {x}{\log (3)}} x^3 \, dx}{\log (3)}+\frac {50 \int e^{\frac {2 x}{\log (3)}} x^3 \, dx}{\log (3)}-\frac {(50 (5-\log (27))) \int e^{\frac {x}{\log (3)}} x^2 \, dx}{\log (3)}+\frac {(25 \log (27)) \int e^{\frac {2 x}{\log (3)}} x^2 \, dx}{\log (3)}-\frac {(125 \log (81)) \int e^{\frac {x}{\log (3)}} x \, dx}{\log (3)} \\ & = 625 x-250 x^2+25 x^3+50 e^{\frac {x}{\log (3)}} x^3+25 e^{\frac {2 x}{\log (3)}} x^3-50 e^{\frac {x}{\log (3)}} x^2 (5-\log (27))+\frac {25}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (27)-125 e^{\frac {x}{\log (3)}} x \log (81)-75 \int e^{\frac {2 x}{\log (3)}} x^2 \, dx-150 \int e^{\frac {x}{\log (3)}} x^2 \, dx+(100 (5-\log (27))) \int e^{\frac {x}{\log (3)}} x \, dx-(25 \log (27)) \int e^{\frac {2 x}{\log (3)}} x \, dx+(125 \log (81)) \int e^{\frac {x}{\log (3)}} \, dx \\ & = 625 x-250 x^2+25 x^3+50 e^{\frac {x}{\log (3)}} x^3+25 e^{\frac {2 x}{\log (3)}} x^3-150 e^{\frac {x}{\log (3)}} x^2 \log (3)-\frac {75}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (3)-50 e^{\frac {x}{\log (3)}} x^2 (5-\log (27))+100 e^{\frac {x}{\log (3)}} x \log (3) (5-\log (27))+\frac {25}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (27)-\frac {25}{2} e^{\frac {2 x}{\log (3)}} x \log (3) \log (27)-125 e^{\frac {x}{\log (3)}} x \log (81)+125 e^{\frac {x}{\log (3)}} \log (3) \log (81)+(75 \log (3)) \int e^{\frac {2 x}{\log (3)}} x \, dx+(300 \log (3)) \int e^{\frac {x}{\log (3)}} x \, dx-(100 \log (3) (5-\log (27))) \int e^{\frac {x}{\log (3)}} \, dx+\frac {1}{2} (25 \log (3) \log (27)) \int e^{\frac {2 x}{\log (3)}} \, dx \\ & = 625 x-250 x^2+25 x^3+50 e^{\frac {x}{\log (3)}} x^3+25 e^{\frac {2 x}{\log (3)}} x^3-150 e^{\frac {x}{\log (3)}} x^2 \log (3)-\frac {75}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (3)+300 e^{\frac {x}{\log (3)}} x \log ^2(3)+\frac {75}{2} e^{\frac {2 x}{\log (3)}} x \log ^2(3)-50 e^{\frac {x}{\log (3)}} x^2 (5-\log (27))+100 e^{\frac {x}{\log (3)}} x \log (3) (5-\log (27))-100 e^{\frac {x}{\log (3)}} \log ^2(3) (5-\log (27))+\frac {25}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (27)-\frac {25}{2} e^{\frac {2 x}{\log (3)}} x \log (3) \log (27)+\frac {25}{4} e^{\frac {2 x}{\log (3)}} \log ^2(3) \log (27)-125 e^{\frac {x}{\log (3)}} x \log (81)+125 e^{\frac {x}{\log (3)}} \log (3) \log (81)-\frac {1}{2} \left (75 \log ^2(3)\right ) \int e^{\frac {2 x}{\log (3)}} \, dx-\left (300 \log ^2(3)\right ) \int e^{\frac {x}{\log (3)}} \, dx \\ & = 625 x-250 x^2+25 x^3+50 e^{\frac {x}{\log (3)}} x^3+25 e^{\frac {2 x}{\log (3)}} x^3-150 e^{\frac {x}{\log (3)}} x^2 \log (3)-\frac {75}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (3)+300 e^{\frac {x}{\log (3)}} x \log ^2(3)+\frac {75}{2} e^{\frac {2 x}{\log (3)}} x \log ^2(3)-300 e^{\frac {x}{\log (3)}} \log ^3(3)-\frac {75}{4} e^{\frac {2 x}{\log (3)}} \log ^3(3)-50 e^{\frac {x}{\log (3)}} x^2 (5-\log (27))+100 e^{\frac {x}{\log (3)}} x \log (3) (5-\log (27))-100 e^{\frac {x}{\log (3)}} \log ^2(3) (5-\log (27))+\frac {25}{2} e^{\frac {2 x}{\log (3)}} x^2 \log (27)-\frac {25}{2} e^{\frac {2 x}{\log (3)}} x \log (3) \log (27)+\frac {25}{4} e^{\frac {2 x}{\log (3)}} \log ^2(3) \log (27)-125 e^{\frac {x}{\log (3)}} x \log (81)+125 e^{\frac {x}{\log (3)}} \log (3) \log (81) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 x \left (-5+x+e^{\frac {x}{\log (3)}} x\right )^2 \]

[In]

Integrate[((25 - 5*x - 5*E^(x/Log[3])*x)^2*((-5 + 3*x)*Log[3] + E^(x/Log[3])*(2*x^2 + 3*x*Log[3])))/((-5 + x)*
Log[3] + E^(x/Log[3])*x*Log[3]),x]

[Out]

25*x*(-5 + x + E^(x/Log[3])*x)^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(47\) vs. \(2(19)=38\).

Time = 0.33 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.29

method	result	size
risch	\(25 \,{\mathrm e}^{\frac {2 x}{\ln \left (3\right )}} x^{3}+25 x^{3}-250 x^{2}+625 x +\left (50 x^{3}-250 x^{2}\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}\)	\(48\)
norman	\(25 \,{\mathrm e}^{\frac {2 x}{\ln \left (3\right )}} x^{3}+50 \,{\mathrm e}^{\frac {x}{\ln \left (3\right )}} x^{3}-250 x^{2} {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+25 x^{3}-250 x^{2}+625 x\)	\(53\)
parallelrisch	\(\frac {625 x \ln \left (3\right )-250 x^{2} \ln \left (3\right )+25 x^{3} \ln \left (3\right )-250 \ln \left (3\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}} x^{2}+50 x^{3} \ln \left (3\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+25 x^{3} \ln \left (3\right ) {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}}}{\ln \left (3\right )}\)	\(70\)
default	\(25 \ln \left (3\right ) \left (-5 x \,{\mathrm e}^{\frac {x}{\ln \left (3\right )}}+\frac {25 x}{\ln \left (3\right )}-\frac {10 x^{2}}{\ln \left (3\right )}+5 \ln \left (3\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+3 x^{2} {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+\frac {x^{3}}{\ln \left (3\right )}+6 \ln \left (3\right )^{2} {\mathrm e}^{\frac {x}{\ln \left (3\right )}}-6 x \ln \left (3\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}\right )+50 \,{\mathrm e}^{\frac {x}{\ln \left (3\right )}} x^{3}+50 \left (-3 \ln \left (3\right )-5\right ) x^{2} {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+25 \,{\mathrm e}^{\frac {2 x}{\ln \left (3\right )}} x^{3}-\frac {75 \ln \left (3\right )^{3} {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}}}{4}+\frac {75 \ln \left (3\right )^{2} {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}} x}{2}-\frac {75 \ln \left (3\right ) {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}} x^{2}}{2}-100 \ln \left (3\right )^{2} \left (3 \ln \left (3\right )+5\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+100 \ln \left (3\right ) \left (3 \ln \left (3\right )+5\right ) x \,{\mathrm e}^{\frac {x}{\ln \left (3\right )}}+75 \ln \left (3\right ) \left (x^{2} {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+\left (-2 \ln \left (3\right )-5\right ) x \,{\mathrm e}^{\frac {x}{\ln \left (3\right )}}+\ln \left (3\right ) \left (2 \ln \left (3\right )+5\right ) {\mathrm e}^{\frac {x}{\ln \left (3\right )}}+\frac {x^{2} {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}}}{2}+\frac {\ln \left (3\right )^{2} {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}}}{4}-\frac {x \ln \left (3\right ) {\mathrm e}^{\frac {2 x}{\ln \left (3\right )}}}{2}\right )\)	\(307\)

[In]

int(((3*x*ln(3)+2*x^2)*exp(x/ln(3))+(3*x-5)*ln(3))*(-5*x*exp(x/ln(3))-5*x+25)^2/(x*ln(3)*exp(x/ln(3))+(-5+x)*l
n(3)),x,method=_RETURNVERBOSE)

[Out]

25*exp(x/ln(3))^2*x^3+25*x^3-250*x^2+625*x+(50*x^3-250*x^2)*exp(x/ln(3))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (17) = 34\).

Time = 0.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.14 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 \, x^{3} e^{\left (\frac {2 \, x}{\log \left (3\right )}\right )} + 25 \, x^{3} - 250 \, x^{2} + 50 \, {\left (x^{3} - 5 \, x^{2}\right )} e^{\frac {x}{\log \left (3\right )}} + 625 \, x \]

[In]

integrate(((3*x*log(3)+2*x^2)*exp(x/log(3))+(3*x-5)*log(3))*(-5*x*exp(x/log(3))-5*x+25)^2/(x*log(3)*exp(x/log(
3))+(-5+x)*log(3)),x, algorithm="fricas")

[Out]

25*x^3*e^(2*x/log(3)) + 25*x^3 - 250*x^2 + 50*(x^3 - 5*x^2)*e^(x/log(3)) + 625*x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (17) = 34\).

Time = 0.12 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.00 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 x^{3} e^{\frac {2 x}{\log {\left (3 \right )}}} + 25 x^{3} - 250 x^{2} + 625 x + \left (50 x^{3} - 250 x^{2}\right ) e^{\frac {x}{\log {\left (3 \right )}}} \]

[In]

integrate(((3*x*ln(3)+2*x**2)*exp(x/ln(3))+(3*x-5)*ln(3))*(-5*x*exp(x/ln(3))-5*x+25)**2/(x*ln(3)*exp(x/ln(3))+
(-5+x)*ln(3)),x)

[Out]

25*x**3*exp(2*x/log(3)) + 25*x**3 - 250*x**2 + 625*x + (50*x**3 - 250*x**2)*exp(x/log(3))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (17) = 34\).

Time = 0.34 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.14 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 \, x^{3} e^{\left (\frac {2 \, x}{\log \left (3\right )}\right )} + 25 \, x^{3} - 250 \, x^{2} + 50 \, {\left (x^{3} - 5 \, x^{2}\right )} e^{\frac {x}{\log \left (3\right )}} + 625 \, x \]

[In]

integrate(((3*x*log(3)+2*x^2)*exp(x/log(3))+(3*x-5)*log(3))*(-5*x*exp(x/log(3))-5*x+25)^2/(x*log(3)*exp(x/log(
3))+(-5+x)*log(3)),x, algorithm="maxima")

[Out]

25*x^3*e^(2*x/log(3)) + 25*x^3 - 250*x^2 + 50*(x^3 - 5*x^2)*e^(x/log(3)) + 625*x

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (17) = 34\).

Time = 0.26 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.43 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25 \, x^{3} e^{\left (\frac {2 \, x}{\log \left (3\right )}\right )} + 50 \, x^{3} e^{\frac {x}{\log \left (3\right )}} + 25 \, x^{3} - 250 \, x^{2} e^{\frac {x}{\log \left (3\right )}} - 250 \, x^{2} + 625 \, x \]

[In]

integrate(((3*x*log(3)+2*x^2)*exp(x/log(3))+(3*x-5)*log(3))*(-5*x*exp(x/log(3))-5*x+25)^2/(x*log(3)*exp(x/log(
3))+(-5+x)*log(3)),x, algorithm="giac")

[Out]

25*x^3*e^(2*x/log(3)) + 50*x^3*e^(x/log(3)) + 25*x^3 - 250*x^2*e^(x/log(3)) - 250*x^2 + 625*x

Mupad [B] (verification not implemented)

Time = 11.39 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {\left (25-5 x-5 e^{\frac {x}{\log (3)}} x\right )^2 \left ((-5+3 x) \log (3)+e^{\frac {x}{\log (3)}} \left (2 x^2+3 x \log (3)\right )\right )}{(-5+x) \log (3)+e^{\frac {x}{\log (3)}} x \log (3)} \, dx=25\,x\,{\left (x+x\,{\mathrm {e}}^{\frac {x}{\ln \left (3\right )}}-5\right )}^2 \]

[In]

int(((log(3)*(3*x - 5) + exp(x/log(3))*(3*x*log(3) + 2*x^2))*(5*x + 5*x*exp(x/log(3)) - 25)^2)/(log(3)*(x - 5)
+ x*exp(x/log(3))*log(3)),x)

[Out]

25*x*(x + x*exp(x/log(3)) - 5)^2