\(\int \frac {e^3 (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {(-x^2+\log (9+3 x)) (e^3 (-75 x^2+5 x^3+7 x^4-x^5)+e^3 (75-5 x-7 x^2+x^3) \log (9+3 x))}{e^3})}{(-x^2+\log (9+3 x)) (-75 x^2+5 x^3+7 x^4-x^5+(75-5 x-7 x^2+x^3) \log (9+3 x))} \, dx\) [7650]

Optimal result

Integrand size = 155, antiderivative size = 30 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=e^3 x+\frac {e^3 x}{(-5+x) \left (-x^2+\log (3 (3+x))\right )} \]

[Out]

x*exp(3)+x/(-5+x)/exp(ln(ln(3*x+9)-x^2)-3)

Rubi [F]

\[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=\int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx \]

[In]

Int[(E^3*(5*x - 16*x^2 + x^3 + 2*x^4 + (-15 - 5*x)*Log[9 + 3*x] + ((-x^2 + Log[9 + 3*x])*(E^3*(-75*x^2 + 5*x^3
+ 7*x^4 - x^5) + E^3*(75 - 5*x - 7*x^2 + x^3)*Log[9 + 3*x]))/E^3))/((-x^2 + Log[9 + 3*x])*(-75*x^2 + 5*x^3 +
7*x^4 - x^5 + (75 - 5*x - 7*x^2 + x^3)*Log[9 + 3*x])),x]

[Out]

E^3*x + (15*E^3*Defer[Int][1/((-5 + x)^2*(x^2 - Log[3*(3 + x)])), x])/8 - (15*E^3*Defer[Int][1/((-5 + x)*(x^2
- Log[3*(3 + x)])), x])/64 + 10*E^3*Defer[Int][(x^2 - Log[9 + 3*x])^(-2), x] + (395*E^3*Defer[Int][1/((-5 + x)
*(x^2 - Log[9 + 3*x])^2), x])/8 + 2*E^3*Defer[Int][x/(x^2 - Log[9 + 3*x])^2, x] - (3*E^3*Defer[Int][1/((3 + x)
*(x^2 - Log[9 + 3*x])^2), x])/8 + (25*E^3*Defer[Int][1/((-5 + x)^2*(x^2 - Log[9 + 3*x])), x])/8 + (15*E^3*Defe
r[Int][1/((-5 + x)*(x^2 - Log[9 + 3*x])), x])/64

Rubi steps \begin{align*} \text {integral}& = e^3 \int \frac {5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx \\ & = e^3 \int \frac {x \left (5-16 x+x^2+77 x^3-5 x^4-7 x^5+x^6\right )-\left (15+5 x+150 x^2-10 x^3-14 x^4+2 x^5\right ) \log (3 (3+x))+(-5+x)^2 (3+x) \log ^2(3 (3+x))}{(5-x)^2 (3+x) \left (x^2-\log (9+3 x)\right )^2} \, dx \\ & = e^3 \int \left (\frac {-5 x+16 x^2-x^3-77 x^4+5 x^5+7 x^6-x^7+15 \log (3 (3+x))+5 x \log (3 (3+x))+150 x^2 \log (3 (3+x))-10 x^3 \log (3 (3+x))-14 x^4 \log (3 (3+x))+2 x^5 \log (3 (3+x))-75 \log ^2(3 (3+x))+5 x \log ^2(3 (3+x))+7 x^2 \log ^2(3 (3+x))-x^3 \log ^2(3 (3+x))}{64 (-5+x) \left (x^2-\log (9+3 x)\right )^2}+\frac {5 x-16 x^2+x^3+77 x^4-5 x^5-7 x^6+x^7-15 \log (3 (3+x))-5 x \log (3 (3+x))-150 x^2 \log (3 (3+x))+10 x^3 \log (3 (3+x))+14 x^4 \log (3 (3+x))-2 x^5 \log (3 (3+x))+75 \log ^2(3 (3+x))-5 x \log ^2(3 (3+x))-7 x^2 \log ^2(3 (3+x))+x^3 \log ^2(3 (3+x))}{8 (-5+x)^2 \left (x^2-\log (9+3 x)\right )^2}+\frac {5 x-16 x^2+x^3+77 x^4-5 x^5-7 x^6+x^7-15 \log (3 (3+x))-5 x \log (3 (3+x))-150 x^2 \log (3 (3+x))+10 x^3 \log (3 (3+x))+14 x^4 \log (3 (3+x))-2 x^5 \log (3 (3+x))+75 \log ^2(3 (3+x))-5 x \log ^2(3 (3+x))-7 x^2 \log ^2(3 (3+x))+x^3 \log ^2(3 (3+x))}{64 (3+x) \left (x^2-\log (9+3 x)\right )^2}\right ) \, dx \\ & = \frac {1}{64} e^3 \int \frac {-5 x+16 x^2-x^3-77 x^4+5 x^5+7 x^6-x^7+15 \log (3 (3+x))+5 x \log (3 (3+x))+150 x^2 \log (3 (3+x))-10 x^3 \log (3 (3+x))-14 x^4 \log (3 (3+x))+2 x^5 \log (3 (3+x))-75 \log ^2(3 (3+x))+5 x \log ^2(3 (3+x))+7 x^2 \log ^2(3 (3+x))-x^3 \log ^2(3 (3+x))}{(-5+x) \left (x^2-\log (9+3 x)\right )^2} \, dx+\frac {1}{64} e^3 \int \frac {5 x-16 x^2+x^3+77 x^4-5 x^5-7 x^6+x^7-15 \log (3 (3+x))-5 x \log (3 (3+x))-150 x^2 \log (3 (3+x))+10 x^3 \log (3 (3+x))+14 x^4 \log (3 (3+x))-2 x^5 \log (3 (3+x))+75 \log ^2(3 (3+x))-5 x \log ^2(3 (3+x))-7 x^2 \log ^2(3 (3+x))+x^3 \log ^2(3 (3+x))}{(3+x) \left (x^2-\log (9+3 x)\right )^2} \, dx+\frac {1}{8} e^3 \int \frac {5 x-16 x^2+x^3+77 x^4-5 x^5-7 x^6+x^7-15 \log (3 (3+x))-5 x \log (3 (3+x))-150 x^2 \log (3 (3+x))+10 x^3 \log (3 (3+x))+14 x^4 \log (3 (3+x))-2 x^5 \log (3 (3+x))+75 \log ^2(3 (3+x))-5 x \log ^2(3 (3+x))-7 x^2 \log ^2(3 (3+x))+x^3 \log ^2(3 (3+x))}{(-5+x)^2 \left (x^2-\log (9+3 x)\right )^2} \, dx \\ & = \frac {1}{64} e^3 \int \frac {x \left (5-16 x+x^2+77 x^3-5 x^4-7 x^5+x^6\right )-\left (15+5 x+150 x^2-10 x^3-14 x^4+2 x^5\right ) \log (3 (3+x))+(-5+x)^2 (3+x) \log ^2(3 (3+x))}{(5-x) \left (x^2-\log (9+3 x)\right )^2} \, dx+\frac {1}{64} e^3 \int \frac {x \left (5-16 x+x^2+77 x^3-5 x^4-7 x^5+x^6\right )-\left (15+5 x+150 x^2-10 x^3-14 x^4+2 x^5\right ) \log (3 (3+x))+(-5+x)^2 (3+x) \log ^2(3 (3+x))}{(3+x) \left (x^2-\log (9+3 x)\right )^2} \, dx+\frac {1}{8} e^3 \int \frac {x \left (5-16 x+x^2+77 x^3-5 x^4-7 x^5+x^6\right )-\left (15+5 x+150 x^2-10 x^3-14 x^4+2 x^5\right ) \log (3 (3+x))+(-5+x)^2 (3+x) \log ^2(3 (3+x))}{(5-x)^2 \left (x^2-\log (9+3 x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=e^3 \left (x+\frac {x}{(-5+x) \left (-x^2+\log (3 (3+x))\right )}\right ) \]

[In]

Integrate[(E^3*(5*x - 16*x^2 + x^3 + 2*x^4 + (-15 - 5*x)*Log[9 + 3*x] + ((-x^2 + Log[9 + 3*x])*(E^3*(-75*x^2 +
5*x^3 + 7*x^4 - x^5) + E^3*(75 - 5*x - 7*x^2 + x^3)*Log[9 + 3*x]))/E^3))/((-x^2 + Log[9 + 3*x])*(-75*x^2 + 5*
x^3 + 7*x^4 - x^5 + (75 - 5*x - 7*x^2 + x^3)*Log[9 + 3*x])),x]

[Out]

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

Maple [A] (verified)

Time = 71.53 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00

method	result	size
risch	\(x \,{\mathrm e}^{3}-\frac {{\mathrm e}^{3} x}{\left (-5+x \right ) \left (x^{2}-\ln \left (3 x +9\right )\right )}\)	\(30\)
default	\(x \,{\mathrm e}^{3}+\frac {{\mathrm e}^{3} x}{\left (-5+x \right ) \left (-\left (3+x \right )^{2}+\ln \left (3\right )+\ln \left (3+x \right )+6 x +9\right )}\)	\(35\)
parts	\(x \,{\mathrm e}^{3}+\frac {{\mathrm e}^{3} x}{\left (-5+x \right ) \left (-\left (3+x \right )^{2}+\ln \left (3\right )+\ln \left (3+x \right )+6 x +9\right )}\)	\(35\)
norman	\(\frac {x^{4} {\mathrm e}^{3}-25 x^{2} {\mathrm e}^{3}+25 \,{\mathrm e}^{3} \ln \left (3 x +9\right )-{\mathrm e}^{3} x^{2} \ln \left (3 x +9\right )-x \,{\mathrm e}^{3}}{\left (-5+x \right ) \left (x^{2}-\ln \left (3 x +9\right )\right )}\)	\(63\)
parallelrisch	\(\frac {\left (12 \,{\mathrm e}^{3} \ln \left (3 x +9\right ) {\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} x^{3}-10 \,{\mathrm e}^{3} \ln \left (3 x +9\right ) {\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} x^{2}+x^{5}-6 \,{\mathrm e}^{3} {\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} x^{5}+5 \,{\mathrm e}^{3} {\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} x^{4}+{\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} x^{6} {\mathrm e}^{3}+5 \ln \left (3 x +9\right )^{2} {\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} {\mathrm e}^{3}-2 \ln \left (3 x +9\right ) x^{3}+\ln \left (3 x +9\right )^{2} x -2 \,{\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} \ln \left (3 x +9\right ) x^{4} {\mathrm e}^{3}+{\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} \ln \left (3 x +9\right )^{2} x^{2} {\mathrm e}^{3}-6 \,{\mathrm e}^{\ln \left (\ln \left (3 x +9\right )-x^{2}\right )-3} \ln \left (3 x +9\right )^{2} x \,{\mathrm e}^{3}\right ) {\mathrm e}^{3}}{\left (-5+x \right ) \left (\ln \left (3 x +9\right )-x^{2}\right ) \left (x^{2}-\ln \left (3 x +9\right )\right )^{2}}\)	\(306\)

[In]

int((((x^3-7*x^2-5*x+75)*exp(3)*ln(3*x+9)+(-x^5+7*x^4+5*x^3-75*x^2)*exp(3))*exp(ln(ln(3*x+9)-x^2)-3)+(-5*x-15)
*ln(3*x+9)+2*x^4+x^3-16*x^2+5*x)/((x^3-7*x^2-5*x+75)*ln(3*x+9)-x^5+7*x^4+5*x^3-75*x^2)/exp(ln(ln(3*x+9)-x^2)-3
),x,method=_RETURNVERBOSE)

[Out]

x*exp(3)-exp(3)*x/(-5+x)/(x^2-ln(3*x+9))

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.90 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=-\frac {{\left (x^{2} - 5 \, x\right )} e^{3} \log \left (3 \, x + 9\right ) - {\left (x^{4} - 5 \, x^{3} - x\right )} e^{3}}{x^{3} - 5 \, x^{2} - {\left (x - 5\right )} \log \left (3 \, x + 9\right )} \]

[In]

integrate((((x^3-7*x^2-5*x+75)*exp(3)*log(3*x+9)+(-x^5+7*x^4+5*x^3-75*x^2)*exp(3))*exp(log(log(3*x+9)-x^2)-3)+
(-5*x-15)*log(3*x+9)+2*x^4+x^3-16*x^2+5*x)/((x^3-7*x^2-5*x+75)*log(3*x+9)-x^5+7*x^4+5*x^3-75*x^2)/exp(log(log(
3*x+9)-x^2)-3),x, algorithm="fricas")

[Out]

-((x^2 - 5*x)*e^3*log(3*x + 9) - (x^4 - 5*x^3 - x)*e^3)/(x^3 - 5*x^2 - (x - 5)*log(3*x + 9))

Sympy [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=x e^{3} + \frac {x e^{3}}{- x^{3} + 5 x^{2} + \left (x - 5\right ) \log {\left (3 x + 9 \right )}} \]

[In]

integrate((((x**3-7*x**2-5*x+75)*exp(3)*ln(3*x+9)+(-x**5+7*x**4+5*x**3-75*x**2)*exp(3))*exp(ln(ln(3*x+9)-x**2)
-3)+(-5*x-15)*ln(3*x+9)+2*x**4+x**3-16*x**2+5*x)/((x**3-7*x**2-5*x+75)*ln(3*x+9)-x**5+7*x**4+5*x**3-75*x**2)/e
xp(ln(ln(3*x+9)-x**2)-3),x)

[Out]

x*exp(3) + x*exp(3)/(-x**3 + 5*x**2 + (x - 5)*log(3*x + 9))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (30) = 60\).

Time = 0.32 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.30 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=\frac {{\left (x^{4} - 5 \, x^{3} - x^{2} \log \left (3\right ) + x {\left (5 \, \log \left (3\right ) - 1\right )} - {\left (x^{2} - 5 \, x\right )} \log \left (x + 3\right )\right )} e^{3}}{x^{3} - 5 \, x^{2} - x \log \left (3\right ) - {\left (x - 5\right )} \log \left (x + 3\right ) + 5 \, \log \left (3\right )} \]

[In]

integrate((((x^3-7*x^2-5*x+75)*exp(3)*log(3*x+9)+(-x^5+7*x^4+5*x^3-75*x^2)*exp(3))*exp(log(log(3*x+9)-x^2)-3)+
(-5*x-15)*log(3*x+9)+2*x^4+x^3-16*x^2+5*x)/((x^3-7*x^2-5*x+75)*log(3*x+9)-x^5+7*x^4+5*x^3-75*x^2)/exp(log(log(
3*x+9)-x^2)-3),x, algorithm="maxima")

[Out]

(x^4 - 5*x^3 - x^2*log(3) + x*(5*log(3) - 1) - (x^2 - 5*x)*log(x + 3))*e^3/(x^3 - 5*x^2 - x*log(3) - (x - 5)*l
og(x + 3) + 5*log(3))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (30) = 60\).

Time = 0.32 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.97 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=\frac {x^{4} e^{3} - 5 \, x^{3} e^{3} - x^{2} e^{3} \log \left (3\right ) - x^{2} e^{3} \log \left (x + 3\right ) + 5 \, x e^{3} \log \left (3\right ) + 5 \, x e^{3} \log \left (x + 3\right ) - x e^{3}}{x^{3} - 5 \, x^{2} - x \log \left (3\right ) - x \log \left (x + 3\right ) + 5 \, \log \left (3\right ) + 5 \, \log \left (x + 3\right )} \]

[In]

integrate((((x^3-7*x^2-5*x+75)*exp(3)*log(3*x+9)+(-x^5+7*x^4+5*x^3-75*x^2)*exp(3))*exp(log(log(3*x+9)-x^2)-3)+
(-5*x-15)*log(3*x+9)+2*x^4+x^3-16*x^2+5*x)/((x^3-7*x^2-5*x+75)*log(3*x+9)-x^5+7*x^4+5*x^3-75*x^2)/exp(log(log(
3*x+9)-x^2)-3),x, algorithm="giac")

[Out]

(x^4*e^3 - 5*x^3*e^3 - x^2*e^3*log(3) - x^2*e^3*log(x + 3) + 5*x*e^3*log(3) + 5*x*e^3*log(x + 3) - x*e^3)/(x^3
- 5*x^2 - x*log(3) - x*log(x + 3) + 5*log(3) + 5*log(x + 3))

Mupad [B] (verification not implemented)

Time = 14.61 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {e^3 \left (5 x-16 x^2+x^3+2 x^4+(-15-5 x) \log (9+3 x)+\frac {\left (-x^2+\log (9+3 x)\right ) \left (e^3 \left (-75 x^2+5 x^3+7 x^4-x^5\right )+e^3 \left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )}{e^3}\right )}{\left (-x^2+\log (9+3 x)\right ) \left (-75 x^2+5 x^3+7 x^4-x^5+\left (75-5 x-7 x^2+x^3\right ) \log (9+3 x)\right )} \, dx=\frac {x\,{\mathrm {e}}^3\,\left (x\,\ln \left (3\,x+9\right )-5\,\ln \left (3\,x+9\right )+5\,x^2-x^3+1\right )}{\left (\ln \left (3\,x+9\right )-x^2\right )\,\left (x-5\right )} \]

[In]

int(-(exp(3 - log(log(3*x + 9) - x^2))*(5*x - log(3*x + 9)*(5*x + 15) - exp(log(log(3*x + 9) - x^2) - 3)*(exp(
3)*(75*x^2 - 5*x^3 - 7*x^4 + x^5) + exp(3)*log(3*x + 9)*(5*x + 7*x^2 - x^3 - 75)) - 16*x^2 + x^3 + 2*x^4))/(lo
g(3*x + 9)*(5*x + 7*x^2 - x^3 - 75) + 75*x^2 - 5*x^3 - 7*x^4 + x^5),x)

[Out]

(x*exp(3)*(x*log(3*x + 9) - 5*log(3*x + 9) + 5*x^2 - x^3 + 1))/((log(3*x + 9) - x^2)*(x - 5))