\(\int \frac {70+40 x-30 x^2+e^x (15 x-5 x^2)+e^x (30+30 x-5 x^2-5 x^3) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x (42 x^3+16 x^4-22 x^5+4 x^6) \log (2+2 x)+e^{2 x} (9 x^3+3 x^4-5 x^5+x^6) \log ^2(2+2 x)} \, dx\) [2071]

Optimal result

Integrand size = 136, antiderivative size = 28 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{x \left (-x+(-3+x) x \left (2+e^x \log (2+2 x)\right )\right )} \]

[Out]

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

Rubi [F]

\[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx \]

[In]

Int[(70 + 40*x - 30*x^2 + E^x*(15*x - 5*x^2) + E^x*(30 + 30*x - 5*x^2 - 5*x^3)*Log[2 + 2*x])/(49*x^3 + 21*x^4
- 24*x^5 + 4*x^6 + E^x*(42*x^3 + 16*x^4 - 22*x^5 + 4*x^6)*Log[2 + 2*x] + E^(2*x)*(9*x^3 + 3*x^4 - 5*x^5 + x^6)
*Log[2 + 2*x]^2),x]

[Out]

(-5*Defer[Int][1/((-3 + x)*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])^2), x])/9 - (100*Defer[Int][1/(x^2*(7 - 2*x
- E^x*(-3 + x)*Log[2*(1 + x)])^2), x])/3 + (95*Defer[Int][1/(x*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])^2), x]
)/9 - 10*Defer[Int][1/(x^3*(-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)])), x] - (10*Defer[Int][1/(x^2*(-7 + 2*x + E
^x*(-3 + x)*Log[2*(1 + x)])), x])/3 + (5*Defer[Int][1/(x*(-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)])), x])/9 - (5
*Defer[Int][1/((-3 + x)*(-7 + 2*x - 3*E^x*Log[2*(1 + x)] + E^x*x*Log[2*(1 + x)])), x])/9 + 45*Defer[Int][1/((-
1 - x)*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])^2*Log[2 + 2*x]), x] + (65*Defer[Int][1/((3 - x)*(7 - 2*x - E^x*
(-3 + x)*Log[2*(1 + x)])^2*Log[2 + 2*x]), x])/12 + (65*Defer[Int][1/((-3 + x)*(7 - 2*x - E^x*(-3 + x)*Log[2*(1
+ x)])^2*Log[2 + 2*x]), x])/12 - 35*Defer[Int][1/(x^2*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])^2*Log[2 + 2*x])
, x] + 45*Defer[Int][1/(x*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])^2*Log[2 + 2*x]), x] + (185*Defer[Int][1/((7
- 2*x - E^x*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x])/36 + (5*Defer[Int][1/((3 - x)*(7 - 2*x - E^x*(-3 + x)*
Log[2*(1 + x)])*Log[2 + 2*x]), x])/12 + (5*Defer[Int][1/((-3 + x)*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])*Log[
2 + 2*x]), x])/12 + 5*Defer[Int][1/(x^2*(7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x] + (35*Defer[
Int][x/((7 - 2*x - E^x*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x])/27 + 5*Defer[Int][1/((1 + x)*(7 - 2*x - E^x
*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x] + (185*Defer[Int][1/((-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)])*Log[
2 + 2*x]), x])/36 + 5*Defer[Int][1/(x*(-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x] + (35*Defer[I
nt][x/((-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)])*Log[2 + 2*x]), x])/27

Rubi steps \begin{align*} \text {integral}& = \int \frac {70+5 \left (8+3 e^x\right ) x-5 \left (6+e^x\right ) x^2-5 e^x \left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{x^3 (1+x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2} \, dx \\ & = \int \left (\frac {5 \left (-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))\right )}{(3-x) x^2 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)}+\frac {5 \left (3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))\right )}{(3-x) x^3 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}\right ) \, dx \\ & = 5 \int \frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{(3-x) x^2 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+5 \int \frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{(3-x) x^3 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx \\ & = 5 \int \frac {-((-3+x) x)-\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{(3-x) x^3 (1+x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+5 \int \frac {-21+13 x-2 x^2-\left (20+7 x-11 x^2+2 x^3\right ) \log (2 (1+x))}{(3-x) x^2 (1+x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx \\ & = 5 \int \left (\frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{108 (3-x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}+\frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{3 x^3 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}+\frac {7 \left (3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))\right )}{27 x \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}+\frac {2 \left (-3 x+x^2-6 \log (2 (1+x))-6 x \log (2 (1+x))+x^2 \log (2 (1+x))+x^3 \log (2 (1+x))\right )}{9 x^2 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}+\frac {-3 x+x^2-6 \log (2 (1+x))-6 x \log (2 (1+x))+x^2 \log (2 (1+x))+x^3 \log (2 (1+x))}{4 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)}\right ) \, dx+5 \int \left (\frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{36 (3-x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)}+\frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{3 x^2 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)}+\frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{4 (1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)}+\frac {2 \left (21-13 x+2 x^2+20 \log (2 (1+x))+7 x \log (2 (1+x))-11 x^2 \log (2 (1+x))+2 x^3 \log (2 (1+x))\right )}{9 x \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)}\right ) \, dx \\ & = \frac {5}{108} \int \frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{(3-x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{36} \int \frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{(3-x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {10}{9} \int \frac {-3 x+x^2-6 \log (2 (1+x))-6 x \log (2 (1+x))+x^2 \log (2 (1+x))+x^3 \log (2 (1+x))}{x^2 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {10}{9} \int \frac {21-13 x+2 x^2+20 \log (2 (1+x))+7 x \log (2 (1+x))-11 x^2 \log (2 (1+x))+2 x^3 \log (2 (1+x))}{x \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {5}{4} \int \frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{(1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {5}{4} \int \frac {-3 x+x^2-6 \log (2 (1+x))-6 x \log (2 (1+x))+x^2 \log (2 (1+x))+x^3 \log (2 (1+x))}{(1+x) \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {35}{27} \int \frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{x \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{3} \int \frac {-21+13 x-2 x^2-20 \log (2 (1+x))-7 x \log (2 (1+x))+11 x^2 \log (2 (1+x))-2 x^3 \log (2 (1+x))}{x^2 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {5}{3} \int \frac {3 x-x^2+6 \log (2 (1+x))+6 x \log (2 (1+x))-x^2 \log (2 (1+x))-x^3 \log (2 (1+x))}{x^3 \left (7-2 x+3 e^x \log (2 (1+x))-e^x x \log (2 (1+x))\right ) \log (2+2 x)} \, dx \\ & = \frac {5}{108} \int \frac {-((-3+x) x)-\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{(3-x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{36} \int \frac {-21+13 x-2 x^2-\left (20+7 x-11 x^2+2 x^3\right ) \log (2 (1+x))}{(3-x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {10}{9} \int \frac {(-3+x) x+\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{x^2 \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {10}{9} \int \frac {21-13 x+2 x^2+\left (20+7 x-11 x^2+2 x^3\right ) \log (2 (1+x))}{x \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {5}{4} \int \frac {(-3+x) x+\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{(1+x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{4} \int \frac {-21+13 x-2 x^2-\left (20+7 x-11 x^2+2 x^3\right ) \log (2 (1+x))}{(1+x) \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx+\frac {35}{27} \int \frac {-((-3+x) x)-\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{x \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{3} \int \frac {-((-3+x) x)-\left (-6-6 x+x^2+x^3\right ) \log (2 (1+x))}{x^3 \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right ) \log (2+2 x)} \, dx+\frac {5}{3} \int \frac {-21+13 x-2 x^2-\left (20+7 x-11 x^2+2 x^3\right ) \log (2 (1+x))}{x^2 \left (7-2 x-e^x (-3+x) \log (2 (1+x))\right )^2 \log (2+2 x)} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 5.15 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{x^2 \left (-7+2 x+e^x (-3+x) \log (2 (1+x))\right )} \]

[In]

Integrate[(70 + 40*x - 30*x^2 + E^x*(15*x - 5*x^2) + E^x*(30 + 30*x - 5*x^2 - 5*x^3)*Log[2 + 2*x])/(49*x^3 + 2
1*x^4 - 24*x^5 + 4*x^6 + E^x*(42*x^3 + 16*x^4 - 22*x^5 + 4*x^6)*Log[2 + 2*x] + E^(2*x)*(9*x^3 + 3*x^4 - 5*x^5
+ x^6)*Log[2 + 2*x]^2),x]

[Out]

5/(x^2*(-7 + 2*x + E^x*(-3 + x)*Log[2*(1 + x)]))

Maple [A] (verified)

Time = 1.42 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18

method	result	size
risch	\(\frac {5}{x^{2} \left (x \,{\mathrm e}^{x} \ln \left (2+2 x \right )-3 \ln \left (2+2 x \right ) {\mathrm e}^{x}+2 x -7\right )}\)	\(33\)
parallelrisch	\(\frac {5}{x^{2} \left (x \,{\mathrm e}^{x} \ln \left (2+2 x \right )-3 \ln \left (2+2 x \right ) {\mathrm e}^{x}+2 x -7\right )}\)	\(33\)

[In]

int(((-5*x^3-5*x^2+30*x+30)*exp(x)*ln(2+2*x)+(-5*x^2+15*x)*exp(x)-30*x^2+40*x+70)/((x^6-5*x^5+3*x^4+9*x^3)*exp
(x)^2*ln(2+2*x)^2+(4*x^6-22*x^5+16*x^4+42*x^3)*exp(x)*ln(2+2*x)+4*x^6-24*x^5+21*x^4+49*x^3),x,method=_RETURNVE
RBOSE)

[Out]

5/x^2/(x*exp(x)*ln(2+2*x)-3*ln(2+2*x)*exp(x)+2*x-7)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{2 \, x^{3} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} \log \left (2 \, x + 2\right ) - 7 \, x^{2}} \]

[In]

integrate(((-5*x^3-5*x^2+30*x+30)*exp(x)*log(2+2*x)+(-5*x^2+15*x)*exp(x)-30*x^2+40*x+70)/((x^6-5*x^5+3*x^4+9*x
^3)*exp(x)^2*log(2+2*x)^2+(4*x^6-22*x^5+16*x^4+42*x^3)*exp(x)*log(2+2*x)+4*x^6-24*x^5+21*x^4+49*x^3),x, algori
thm="fricas")

[Out]

5/(2*x^3 + (x^3 - 3*x^2)*e^x*log(2*x + 2) - 7*x^2)

Sympy [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{2 x^{3} - 7 x^{2} + \left (x^{3} \log {\left (2 x + 2 \right )} - 3 x^{2} \log {\left (2 x + 2 \right )}\right ) e^{x}} \]

[In]

integrate(((-5*x**3-5*x**2+30*x+30)*exp(x)*ln(2+2*x)+(-5*x**2+15*x)*exp(x)-30*x**2+40*x+70)/((x**6-5*x**5+3*x*
*4+9*x**3)*exp(x)**2*ln(2+2*x)**2+(4*x**6-22*x**5+16*x**4+42*x**3)*exp(x)*ln(2+2*x)+4*x**6-24*x**5+21*x**4+49*
x**3),x)

[Out]

5/(2*x**3 - 7*x**2 + (x**3*log(2*x + 2) - 3*x**2*log(2*x + 2))*exp(x))

Maxima [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.71 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{2 \, x^{3} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} \log \left (x + 1\right ) - 7 \, x^{2} + {\left (x^{3} \log \left (2\right ) - 3 \, x^{2} \log \left (2\right )\right )} e^{x}} \]

[In]

integrate(((-5*x^3-5*x^2+30*x+30)*exp(x)*log(2+2*x)+(-5*x^2+15*x)*exp(x)-30*x^2+40*x+70)/((x^6-5*x^5+3*x^4+9*x
^3)*exp(x)^2*log(2+2*x)^2+(4*x^6-22*x^5+16*x^4+42*x^3)*exp(x)*log(2+2*x)+4*x^6-24*x^5+21*x^4+49*x^3),x, algori
thm="maxima")

[Out]

5/(2*x^3 + (x^3 - 3*x^2)*e^x*log(x + 1) - 7*x^2 + (x^3*log(2) - 3*x^2*log(2))*e^x)

Giac [A] (verification not implemented)

none

Time = 0.34 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.43 \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\frac {5}{x^{3} e^{x} \log \left (2 \, x + 2\right ) - 3 \, x^{2} e^{x} \log \left (2 \, x + 2\right ) + 2 \, x^{3} - 7 \, x^{2}} \]

[In]

integrate(((-5*x^3-5*x^2+30*x+30)*exp(x)*log(2+2*x)+(-5*x^2+15*x)*exp(x)-30*x^2+40*x+70)/((x^6-5*x^5+3*x^4+9*x
^3)*exp(x)^2*log(2+2*x)^2+(4*x^6-22*x^5+16*x^4+42*x^3)*exp(x)*log(2+2*x)+4*x^6-24*x^5+21*x^4+49*x^3),x, algori
thm="giac")

[Out]

5/(x^3*e^x*log(2*x + 2) - 3*x^2*e^x*log(2*x + 2) + 2*x^3 - 7*x^2)

Mupad [F(-1)]

Timed out. \[ \int \frac {70+40 x-30 x^2+e^x \left (15 x-5 x^2\right )+e^x \left (30+30 x-5 x^2-5 x^3\right ) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x \left (42 x^3+16 x^4-22 x^5+4 x^6\right ) \log (2+2 x)+e^{2 x} \left (9 x^3+3 x^4-5 x^5+x^6\right ) \log ^2(2+2 x)} \, dx=\int \frac {40\,x+{\mathrm {e}}^x\,\left (15\,x-5\,x^2\right )-30\,x^2+{\mathrm {e}}^x\,\ln \left (2\,x+2\right )\,\left (-5\,x^3-5\,x^2+30\,x+30\right )+70}{49\,x^3+21\,x^4-24\,x^5+4\,x^6+{\mathrm {e}}^x\,\ln \left (2\,x+2\right )\,\left (4\,x^6-22\,x^5+16\,x^4+42\,x^3\right )+{\mathrm {e}}^{2\,x}\,{\ln \left (2\,x+2\right )}^2\,\left (x^6-5\,x^5+3\,x^4+9\,x^3\right )} \,d x \]

[In]

int((40*x + exp(x)*(15*x - 5*x^2) - 30*x^2 + exp(x)*log(2*x + 2)*(30*x - 5*x^2 - 5*x^3 + 30) + 70)/(49*x^3 + 2
1*x^4 - 24*x^5 + 4*x^6 + exp(x)*log(2*x + 2)*(42*x^3 + 16*x^4 - 22*x^5 + 4*x^6) + exp(2*x)*log(2*x + 2)^2*(9*x
^3 + 3*x^4 - 5*x^5 + x^6)),x)

[Out]

int((40*x + exp(x)*(15*x - 5*x^2) - 30*x^2 + exp(x)*log(2*x + 2)*(30*x - 5*x^2 - 5*x^3 + 30) + 70)/(49*x^3 + 2
1*x^4 - 24*x^5 + 4*x^6 + exp(x)*log(2*x + 2)*(42*x^3 + 16*x^4 - 22*x^5 + 4*x^6) + exp(2*x)*log(2*x + 2)^2*(9*x
^3 + 3*x^4 - 5*x^5 + x^6)), x)