∫ −54x+81x3+e8(−6x+9x3)+e2x(−5x−6x2+9x3)+e4(−36x+54x3)+ex(−2+30x+18x2−54x3+e4(10x+6x2−18x3))+(36x−54x3+e4(12x−18x3)+ex(−10x−6x2+18x3)) log(x)+(−6x+9x3) log2(x)_________________________________________________________________________________________________________________________________________ 81x3+54e4x3+9e8x3+e2x(x−6x2+9x3)+ex(18x2−54x3+e4(6x2−18x3))+(−54x3−18e4x3+ex(−6x2+18x3)) log(x)+9x3 log2(x) dx

3.35.6 \(\int \frac {-54 x+81 x^3+e^8 (-6 x+9 x^3)+e^{2 x} (-5 x-6 x^2+9 x^3)+e^4 (-36 x+54 x^3)+e^x (-2+30 x+18 x^2-54 x^3+e^4 (10 x+6 x^2-18 x^3))+(36 x-54 x^3+e^4 (12 x-18 x^3)+e^x (-10 x-6 x^2+18 x^3)) \log (x)+(-6 x+9 x^3) \log ^2(x)}{81 x^3+54 e^4 x^3+9 e^8 x^3+e^{2 x} (x-6 x^2+9 x^3)+e^x (18 x^2-54 x^3+e^4 (6 x^2-18 x^3))+(-54 x^3-18 e^4 x^3+e^x (-6 x^2+18 x^3)) \log (x)+9 x^3 \log ^2(x)} \, dx\)

Optimal. Leaf size=30 \[ 5+x+\frac {2}{3 x-\frac {e^x}{-3-e^4+e^x+\log (x)}} \]

________________________________________________________________________________________

Rubi [F] time = 30.74, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-54 x+81 x^3+e^8 \left (-6 x+9 x^3\right )+e^{2 x} \left (-5 x-6 x^2+9 x^3\right )+e^4 \left (-36 x+54 x^3\right )+e^x \left (-2+30 x+18 x^2-54 x^3+e^4 \left (10 x+6 x^2-18 x^3\right )\right )+\left (36 x-54 x^3+e^4 \left (12 x-18 x^3\right )+e^x \left (-10 x-6 x^2+18 x^3\right )\right ) \log (x)+\left (-6 x+9 x^3\right ) \log ^2(x)}{81 x^3+54 e^4 x^3+9 e^8 x^3+e^{2 x} \left (x-6 x^2+9 x^3\right )+e^x \left (18 x^2-54 x^3+e^4 \left (6 x^2-18 x^3\right )\right )+\left (-54 x^3-18 e^4 x^3+e^x \left (-6 x^2+18 x^3\right )\right ) \log (x)+9 x^3 \log ^2(x)} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-54*x + 81*x^3 + E^8*(-6*x + 9*x^3) + E^(2*x)*(-5*x - 6*x^2 + 9*x^3) + E^4*(-36*x + 54*x^3) + E^x*(-2 + 3

0*x + 18*x^2 - 54*x^3 + E^4*(10*x + 6*x^2 - 18*x^3)) + (36*x - 54*x^3 + E^4*(12*x - 18*x^3) + E^x*(-10*x - 6*x

^2 + 18*x^3))*Log[x] + (-6*x + 9*x^3)*Log[x]^2)/(81*x^3 + 54*E^4*x^3 + 9*E^8*x^3 + E^(2*x)*(x - 6*x^2 + 9*x^3)

+ E^x*(18*x^2 - 54*x^3 + E^4*(6*x^2 - 18*x^3)) + (-54*x^3 - 18*E^4*x^3 + E^x*(-6*x^2 + 18*x^3))*Log[x] + 9*x^

3*Log[x]^2),x]

[Out]

-2/(1 - 3*x) + x - 2*(3 + E^4)^2*Defer[Int][(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^(-2), x] + 2*E^4*(3

+ E^4)*Defer[Int][1/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] - 6*(2 + E^4)*(3 + E^4

)*Defer[Int][1/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] - 2*(3 + E^4)^2*Defer[Int][1

/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] + 2*E^4*(3 + E^4)*Defer[Int][1/((-1 + 3*x)

*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] - 4*(3 + E^4)^2*Defer[Int][1/((-1 + 3*x)*(E^x - 3*E^x*x

+ 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] + 4*(3 + E^4)*Defer[Int][Log[x]/(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x

*Log[x])^2, x] + 4*(3 + E^4)*Defer[Int][Log[x]/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2),

x] - 2*(3 + 2*E^4)*Defer[Int][Log[x]/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] + 6*(

5 + 2*E^4)*Defer[Int][Log[x]/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] + 8*(3 + E^4)*

Defer[Int][Log[x]/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] - 2*(3 + 2*E^4)*Defer[Int]

[Log[x]/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x] - 2*Defer[Int][Log[x]^2/(E^x - 3*E^x

*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2, x] - 6*Defer[Int][Log[x]^2/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x

- 3*x*Log[x])^2), x] - 2*Defer[Int][Log[x]^2/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^2), x

] + 2*(3 + E^4)*Defer[Int][(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^(-1), x] + 2*(18 + 5*E^4)*Defer[Int]

[(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])^(-1), x] + 2*(3 + E^4)*Defer[Int][1/((1 - 3*x)^2*(E^x - 3*E^x*

x + 9*(1 + E^4/3)*x - 3*x*Log[x])), x] + 2*(18 + 5*E^4)*Defer[Int][1/((1 - 3*x)^2*(E^x - 3*E^x*x + 9*(1 + E^4/

3)*x - 3*x*Log[x])), x] + 2*(3 + E^4)*Defer[Int][1/((1 - 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])),

x] + 2*(18 + 5*E^4)*Defer[Int][1/((1 - 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])), x] + 6*(3 + E^4)

*Defer[Int][x/(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x]), x] + 6*Defer[Int][1/((-1 + 3*x)*(E^x - 3*E^x*x +

9*(1 + E^4/3)*x - 3*x*Log[x])), x] + 4*(3 + E^4)*Defer[Int][1/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x -

3*x*Log[x])), x] + 2*(18 + 5*E^4)*Defer[Int][1/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])), x]

+ 12*Defer[Int][Log[x]/(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x]), x] + 14*Defer[Int][Log[x]/((1 - 3*x)*(

E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])), x] + 6*Defer[Int][(x*Log[x])/(E^x - 3*E^x*x + 9*(1 + E^4/3)*x

- 3*x*Log[x]), x] + 12*Defer[Int][Log[x]/((-1 + 3*x)*(E^x - 3*E^x*x + 9*(1 + E^4/3)*x - 3*x*Log[x])), x] + 2*(

3 + E^4)*Defer[Int][(-E^x + 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Log[x])^(-1), x] + 2*(18 + 5*E^4)*Defer[Int][(-E^x

+ 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Log[x])^(-1), x] + 6*Defer[Int][1/((1 - 3*x)^2*(-E^x + 3*E^x*x - 9*(1 + E^4

/3)*x + 3*x*Log[x])), x] + 2*Defer[Int][1/(x*(-E^x + 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Log[x])), x] + 6*(3 + E^4

)*Defer[Int][x/(-E^x + 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Log[x]), x] + 12*Defer[Int][Log[x]/(-E^x + 3*E^x*x - 9*

(1 + E^4/3)*x + 3*x*Log[x]), x] + 12*Defer[Int][Log[x]/((1 - 3*x)^2*(-E^x + 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Lo

g[x])), x] + 6*Defer[Int][(x*Log[x])/(-E^x + 3*E^x*x - 9*(1 + E^4/3)*x + 3*x*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-54 x+81 x^3+e^8 \left (-6 x+9 x^3\right )+e^{2 x} \left (-5 x-6 x^2+9 x^3\right )+e^4 \left (-36 x+54 x^3\right )+e^x \left (-2+30 x+18 x^2-54 x^3+e^4 \left (10 x+6 x^2-18 x^3\right )\right )+\left (36 x-54 x^3+e^4 \left (12 x-18 x^3\right )+e^x \left (-10 x-6 x^2+18 x^3\right )\right ) \log (x)+\left (-6 x+9 x^3\right ) \log ^2(x)}{9 e^8 x^3+\left (81+54 e^4\right ) x^3+e^{2 x} \left (x-6 x^2+9 x^3\right )+e^x \left (18 x^2-54 x^3+e^4 \left (6 x^2-18 x^3\right )\right )+\left (-54 x^3-18 e^4 x^3+e^x \left (-6 x^2+18 x^3\right )\right ) \log (x)+9 x^3 \log ^2(x)} \, dx\\ &=\int \frac {-54 x+81 x^3+e^8 \left (-6 x+9 x^3\right )+e^{2 x} \left (-5 x-6 x^2+9 x^3\right )+e^4 \left (-36 x+54 x^3\right )+e^x \left (-2+30 x+18 x^2-54 x^3+e^4 \left (10 x+6 x^2-18 x^3\right )\right )+\left (36 x-54 x^3+e^4 \left (12 x-18 x^3\right )+e^x \left (-10 x-6 x^2+18 x^3\right )\right ) \log (x)+\left (-6 x+9 x^3\right ) \log ^2(x)}{\left (81+54 e^4+9 e^8\right ) x^3+e^{2 x} \left (x-6 x^2+9 x^3\right )+e^x \left (18 x^2-54 x^3+e^4 \left (6 x^2-18 x^3\right )\right )+\left (-54 x^3-18 e^4 x^3+e^x \left (-6 x^2+18 x^3\right )\right ) \log (x)+9 x^3 \log ^2(x)} \, dx\\ &=\int \frac {27 \left (1+\frac {1}{9} e^4 \left (6+e^4\right )\right ) x \left (-2+3 x^2\right )+e^{2 x} x \left (-5-6 x+9 x^2\right )-2 e^{4+x} x \left (-5-3 x+9 x^2\right )+e^x \left (-2+30 x+18 x^2-54 x^3\right )+2 x \left (18-27 x^2+e^4 \left (6-9 x^2\right )+e^x \left (-5-3 x+9 x^2\right )\right ) \log (x)+\left (-6 x+9 x^3\right ) \log ^2(x)}{x \left (9 \left (1+\frac {e^4}{3}\right ) x-e^x (-1+3 x)-3 x \log (x)\right )^2} \, dx\\ &=\int \left (\frac {-5-6 x+9 x^2}{(-1+3 x)^2}+\frac {2 \left (-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)\right )}{(1-3 x)^2 x \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )}+\frac {6 \left (3 \left (1+\frac {e^4}{3}\right )-\log (x)\right ) \left (-2 \left (1+\frac {e^4}{2}\right )+e^4 x-9 \left (1+\frac {e^4}{3}\right ) x^2+\log (x)-x \log (x)+3 x^2 \log (x)\right )}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}\right ) \, dx\\ &=2 \int \frac {-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)}{(1-3 x)^2 x \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )} \, dx+6 \int \frac {\left (3 \left (1+\frac {e^4}{3}\right )-\log (x)\right ) \left (-2 \left (1+\frac {e^4}{2}\right )+e^4 x-9 \left (1+\frac {e^4}{3}\right ) x^2+\log (x)-x \log (x)+3 x^2 \log (x)\right )}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+\int \frac {-5-6 x+9 x^2}{(-1+3 x)^2} \, dx\\ &=2 \int \left (\frac {3 \left (-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)\right )}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )}+\frac {3 \left (-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)\right )}{(1-3 x) \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )}+\frac {-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)}{x \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )}\right ) \, dx+6 \int \left (\frac {\left (-3-e^4\right ) \left (2+e^4\right )}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}+\frac {e^4 \left (3+e^4\right ) x}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}-\frac {3 \left (3+e^4\right )^2 x^2}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}+\frac {\left (2+e^4\right ) \left (1+\frac {3+e^4}{2+e^4}\right ) \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}-\frac {\left (2+\frac {3}{e^4}\right ) e^4 x \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}+\frac {6 \left (3+e^4\right ) x^2 \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}-\frac {\log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}+\frac {x \log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}-\frac {3 x^2 \log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2}\right ) \, dx+\int \left (1-\frac {6}{(-1+3 x)^2}\right ) \, dx\\ &=-\frac {2}{1-3 x}+x+2 \int \frac {-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)}{x \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )} \, dx-6 \int \frac {\log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+6 \int \frac {x \log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+6 \int \frac {-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )} \, dx+6 \int \frac {-1+18 \left (1+\frac {5 e^4}{18}\right ) x+9 \left (1+\frac {e^4}{3}\right ) x^2-5 x \log (x)-3 x^2 \log (x)}{(1-3 x) \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )} \, dx-18 \int \frac {x^2 \log ^2(x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+\left (36 \left (3+e^4\right )\right ) \int \frac {x^2 \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+\left (6 e^4 \left (3+e^4\right )\right ) \int \frac {x}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx-\left (6 \left (2+e^4\right ) \left (3+e^4\right )\right ) \int \frac {1}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx-\left (18 \left (3+e^4\right )^2\right ) \int \frac {x^2}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx-\left (6 \left (3+2 e^4\right )\right ) \int \frac {x \log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx+\left (6 \left (5+2 e^4\right )\right ) \int \frac {\log (x)}{(1-3 x)^2 \left (e^x-3 e^x x+9 \left (1+\frac {e^4}{3}\right ) x-3 x \log (x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A] time = 0.23, size = 47, normalized size = 1.57 \begin {gather*} \frac {2}{3 x}+x+\frac {2 e^x}{3 x \left (-e^x-9 x-3 e^4 x+3 e^x x+3 x \log (x)\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-54*x + 81*x^3 + E^8*(-6*x + 9*x^3) + E^(2*x)*(-5*x - 6*x^2 + 9*x^3) + E^4*(-36*x + 54*x^3) + E^x*(

-2 + 30*x + 18*x^2 - 54*x^3 + E^4*(10*x + 6*x^2 - 18*x^3)) + (36*x - 54*x^3 + E^4*(12*x - 18*x^3) + E^x*(-10*x

- 6*x^2 + 18*x^3))*Log[x] + (-6*x + 9*x^3)*Log[x]^2)/(81*x^3 + 54*E^4*x^3 + 9*E^8*x^3 + E^(2*x)*(x - 6*x^2 +

9*x^3) + E^x*(18*x^2 - 54*x^3 + E^4*(6*x^2 - 18*x^3)) + (-54*x^3 - 18*E^4*x^3 + E^x*(-6*x^2 + 18*x^3))*Log[x]

+ 9*x^3*Log[x]^2),x]

[Out]

2/(3*x) + x + (2*E^x)/(3*x*(-E^x - 9*x - 3*E^4*x + 3*E^x*x + 3*x*Log[x]))

________________________________________________________________________________________

fricas [B] time = 0.56, size = 68, normalized size = 2.27 \begin {gather*} \frac {9 \, x^{2} + {\left (3 \, x^{2} + 2\right )} e^{4} - {\left (3 \, x^{2} - x + 2\right )} e^{x} - {\left (3 \, x^{2} + 2\right )} \log \relax (x) + 6}{3 \, x e^{4} - {\left (3 \, x - 1\right )} e^{x} - 3 \, x \log \relax (x) + 9 \, x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((9*x^3-6*x)*log(x)^2+((18*x^3-6*x^2-10*x)*exp(x)+(-18*x^3+12*x)*exp(4)-54*x^3+36*x)*log(x)+(9*x^3-6

*x^2-5*x)*exp(x)^2+((-18*x^3+6*x^2+10*x)*exp(4)-54*x^3+18*x^2+30*x-2)*exp(x)+(9*x^3-6*x)*exp(4)^2+(54*x^3-36*x

)*exp(4)+81*x^3-54*x)/(9*x^3*log(x)^2+((18*x^3-6*x^2)*exp(x)-18*x^3*exp(4)-54*x^3)*log(x)+(9*x^3-6*x^2+x)*exp(

x)^2+((-18*x^3+6*x^2)*exp(4)-54*x^3+18*x^2)*exp(x)+9*x^3*exp(4)^2+54*x^3*exp(4)+81*x^3),x, algorithm="fricas")

[Out]

(9*x^2 + (3*x^2 + 2)*e^4 - (3*x^2 - x + 2)*e^x - (3*x^2 + 2)*log(x) + 6)/(3*x*e^4 - (3*x - 1)*e^x - 3*x*log(x)

+ 9*x)

________________________________________________________________________________________

giac [B] time = 0.44, size = 82, normalized size = 2.73 \begin {gather*} \frac {3 \, x^{2} e^{4} - 3 \, x^{2} e^{x} - 3 \, x^{2} \log \relax (x) + 9 \, x^{2} + 3 \, x e^{4} - 2 \, x e^{x} - 3 \, x \log \relax (x) + 9 \, x + 2 \, e^{4} - e^{x} - 2 \, \log \relax (x) + 6}{3 \, x e^{4} - 3 \, x e^{x} - 3 \, x \log \relax (x) + 9 \, x + e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((9*x^3-6*x)*log(x)^2+((18*x^3-6*x^2-10*x)*exp(x)+(-18*x^3+12*x)*exp(4)-54*x^3+36*x)*log(x)+(9*x^3-6

*x^2-5*x)*exp(x)^2+((-18*x^3+6*x^2+10*x)*exp(4)-54*x^3+18*x^2+30*x-2)*exp(x)+(9*x^3-6*x)*exp(4)^2+(54*x^3-36*x

)*exp(4)+81*x^3-54*x)/(9*x^3*log(x)^2+((18*x^3-6*x^2)*exp(x)-18*x^3*exp(4)-54*x^3)*log(x)+(9*x^3-6*x^2+x)*exp(

x)^2+((-18*x^3+6*x^2)*exp(4)-54*x^3+18*x^2)*exp(x)+9*x^3*exp(4)^2+54*x^3*exp(4)+81*x^3),x, algorithm="giac")

[Out]

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

+ 6)/(3*x*e^4 - 3*x*e^x - 3*x*log(x) + 9*x + e^x)

________________________________________________________________________________________

maple [A] time = 0.05, size = 44, normalized size = 1.47


method	result	size

risch	\(\frac {3 x^{2}+2}{3 x}-\frac {2 \,{\mathrm e}^{x}}{3 x \left (3 x \,{\mathrm e}^{4}-3 \,{\mathrm e}^{x} x -3 x \ln \relax (x )+9 x +{\mathrm e}^{x}\right )}\)	\(44\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((9*x^3-6*x)*ln(x)^2+((18*x^3-6*x^2-10*x)*exp(x)+(-18*x^3+12*x)*exp(4)-54*x^3+36*x)*ln(x)+(9*x^3-6*x^2-5*x

)*exp(x)^2+((-18*x^3+6*x^2+10*x)*exp(4)-54*x^3+18*x^2+30*x-2)*exp(x)+(9*x^3-6*x)*exp(4)^2+(54*x^3-36*x)*exp(4)

+81*x^3-54*x)/(9*x^3*ln(x)^2+((18*x^3-6*x^2)*exp(x)-18*x^3*exp(4)-54*x^3)*ln(x)+(9*x^3-6*x^2+x)*exp(x)^2+((-18

*x^3+6*x^2)*exp(4)-54*x^3+18*x^2)*exp(x)+9*x^3*exp(4)^2+54*x^3*exp(4)+81*x^3),x,method=_RETURNVERBOSE)

[Out]

1/3*(3*x^2+2)/x-2/3/x*exp(x)/(3*x*exp(4)-3*exp(x)*x-3*x*ln(x)+9*x+exp(x))

________________________________________________________________________________________

maxima [B] time = 0.58, size = 65, normalized size = 2.17 \begin {gather*} \frac {3 \, x^{2} {\left (e^{4} + 3\right )} - {\left (3 \, x^{2} - x + 2\right )} e^{x} - {\left (3 \, x^{2} + 2\right )} \log \relax (x) + 2 \, e^{4} + 6}{3 \, x {\left (e^{4} + 3\right )} - {\left (3 \, x - 1\right )} e^{x} - 3 \, x \log \relax (x)} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((9*x^3-6*x)*log(x)^2+((18*x^3-6*x^2-10*x)*exp(x)+(-18*x^3+12*x)*exp(4)-54*x^3+36*x)*log(x)+(9*x^3-6

*x^2-5*x)*exp(x)^2+((-18*x^3+6*x^2+10*x)*exp(4)-54*x^3+18*x^2+30*x-2)*exp(x)+(9*x^3-6*x)*exp(4)^2+(54*x^3-36*x

)*exp(4)+81*x^3-54*x)/(9*x^3*log(x)^2+((18*x^3-6*x^2)*exp(x)-18*x^3*exp(4)-54*x^3)*log(x)+(9*x^3-6*x^2+x)*exp(

x)^2+((-18*x^3+6*x^2)*exp(4)-54*x^3+18*x^2)*exp(x)+9*x^3*exp(4)^2+54*x^3*exp(4)+81*x^3),x, algorithm="maxima")

[Out]

(3*x^2*(e^4 + 3) - (3*x^2 - x + 2)*e^x - (3*x^2 + 2)*log(x) + 2*e^4 + 6)/(3*x*(e^4 + 3) - (3*x - 1)*e^x - 3*x*

log(x))

________________________________________________________________________________________

mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {54\,x+{\ln \relax (x)}^2\,\left (6\,x-9\,x^3\right )+{\mathrm {e}}^8\,\left (6\,x-9\,x^3\right )+{\mathrm {e}}^4\,\left (36\,x-54\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (-9\,x^3+6\,x^2+5\,x\right )-{\mathrm {e}}^x\,\left (30\,x+{\mathrm {e}}^4\,\left (-18\,x^3+6\,x^2+10\,x\right )+18\,x^2-54\,x^3-2\right )-\ln \relax (x)\,\left (36\,x+{\mathrm {e}}^4\,\left (12\,x-18\,x^3\right )-54\,x^3-{\mathrm {e}}^x\,\left (-18\,x^3+6\,x^2+10\,x\right )\right )-81\,x^3}{9\,x^3\,{\ln \relax (x)}^2-\ln \relax (x)\,\left ({\mathrm {e}}^x\,\left (6\,x^2-18\,x^3\right )+18\,x^3\,{\mathrm {e}}^4+54\,x^3\right )+{\mathrm {e}}^x\,\left ({\mathrm {e}}^4\,\left (6\,x^2-18\,x^3\right )+18\,x^2-54\,x^3\right )+54\,x^3\,{\mathrm {e}}^4+9\,x^3\,{\mathrm {e}}^8+81\,x^3+{\mathrm {e}}^{2\,x}\,\left (9\,x^3-6\,x^2+x\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(54*x + log(x)^2*(6*x - 9*x^3) + exp(8)*(6*x - 9*x^3) + exp(4)*(36*x - 54*x^3) + exp(2*x)*(5*x + 6*x^2 -

9*x^3) - exp(x)*(30*x + exp(4)*(10*x + 6*x^2 - 18*x^3) + 18*x^2 - 54*x^3 - 2) - log(x)*(36*x + exp(4)*(12*x -

18*x^3) - 54*x^3 - exp(x)*(10*x + 6*x^2 - 18*x^3)) - 81*x^3)/(9*x^3*log(x)^2 - log(x)*(exp(x)*(6*x^2 - 18*x^3)

+ 18*x^3*exp(4) + 54*x^3) + exp(x)*(exp(4)*(6*x^2 - 18*x^3) + 18*x^2 - 54*x^3) + 54*x^3*exp(4) + 9*x^3*exp(8)

+ 81*x^3 + exp(2*x)*(x - 6*x^2 + 9*x^3)),x)

[Out]

int(-(54*x + log(x)^2*(6*x - 9*x^3) + exp(8)*(6*x - 9*x^3) + exp(4)*(36*x - 54*x^3) + exp(2*x)*(5*x + 6*x^2 -

9*x^3) - exp(x)*(30*x + exp(4)*(10*x + 6*x^2 - 18*x^3) + 18*x^2 - 54*x^3 - 2) - log(x)*(36*x + exp(4)*(12*x -

18*x^3) - 54*x^3 - exp(x)*(10*x + 6*x^2 - 18*x^3)) - 81*x^3)/(9*x^3*log(x)^2 - log(x)*(exp(x)*(6*x^2 - 18*x^3)

+ 18*x^3*exp(4) + 54*x^3) + exp(x)*(exp(4)*(6*x^2 - 18*x^3) + 18*x^2 - 54*x^3) + 54*x^3*exp(4) + 9*x^3*exp(8)

+ 81*x^3 + exp(2*x)*(x - 6*x^2 + 9*x^3)), x)

________________________________________________________________________________________

sympy [B] time = 0.64, size = 71, normalized size = 2.37 \begin {gather*} x + \frac {- 2 \log {\relax (x )} + 6 + 2 e^{4}}{9 x^{2} \log {\relax (x )} - 9 x^{2} e^{4} - 27 x^{2} - 3 x \log {\relax (x )} + 9 x + 3 x e^{4} + \left (9 x^{2} - 6 x + 1\right ) e^{x}} + \frac {2}{3 x - 1} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((9*x**3-6*x)*ln(x)**2+((18*x**3-6*x**2-10*x)*exp(x)+(-18*x**3+12*x)*exp(4)-54*x**3+36*x)*ln(x)+(9*x

**3-6*x**2-5*x)*exp(x)**2+((-18*x**3+6*x**2+10*x)*exp(4)-54*x**3+18*x**2+30*x-2)*exp(x)+(9*x**3-6*x)*exp(4)**2

+(54*x**3-36*x)*exp(4)+81*x**3-54*x)/(9*x**3*ln(x)**2+((18*x**3-6*x**2)*exp(x)-18*x**3*exp(4)-54*x**3)*ln(x)+(

9*x**3-6*x**2+x)*exp(x)**2+((-18*x**3+6*x**2)*exp(4)-54*x**3+18*x**2)*exp(x)+9*x**3*exp(4)**2+54*x**3*exp(4)+8

1*x**3),x)

[Out]

x + (-2*log(x) + 6 + 2*exp(4))/(9*x**2*log(x) - 9*x**2*exp(4) - 27*x**2 - 3*x*log(x) + 9*x + 3*x*exp(4) + (9*x

**2 - 6*x + 1)*exp(x)) + 2/(3*x - 1)

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]