3.38.63 \(\int \frac {48+e^{8 x} (3-x)+80 x+40 x^2-5 x^4-x^5+e^{6 x} (24+4 x-4 x^2)+e^{4 x} (72+48 x-6 x^2-6 x^3)+e^{2 x} (96+112 x+24 x^2-12 x^3-4 x^4)+(-112 x-144 x^2-48 x^3+4 x^4+3 x^5+e^{8 x} (-25 x+8 x^2)+e^{6 x} (-164 x-24 x^2+24 x^3)+e^{4 x} (-384 x-228 x^2+30 x^3+24 x^4)+e^{2 x} (-368 x-368 x^2-60 x^3+32 x^4+8 x^5)) \log (x)+(54 x-36 x^2+6 x^3) \log ^2(x)}{(27 x-18 x^2+3 x^3) \log ^2(x)} \, dx\)

Optimal. Leaf size=29 \[ 2 (4+x)+\frac {\left (2+e^{2 x}+x\right )^4}{3 (-3+x) \log (x)} \]

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Rubi [F]  time = 6.68, 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 {48+e^{8 x} (3-x)+80 x+40 x^2-5 x^4-x^5+e^{6 x} \left (24+4 x-4 x^2\right )+e^{4 x} \left (72+48 x-6 x^2-6 x^3\right )+e^{2 x} \left (96+112 x+24 x^2-12 x^3-4 x^4\right )+\left (-112 x-144 x^2-48 x^3+4 x^4+3 x^5+e^{8 x} \left (-25 x+8 x^2\right )+e^{6 x} \left (-164 x-24 x^2+24 x^3\right )+e^{4 x} \left (-384 x-228 x^2+30 x^3+24 x^4\right )+e^{2 x} \left (-368 x-368 x^2-60 x^3+32 x^4+8 x^5\right )\right ) \log (x)+\left (54 x-36 x^2+6 x^3\right ) \log ^2(x)}{\left (27 x-18 x^2+3 x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(48 + E^(8*x)*(3 - x) + 80*x + 40*x^2 - 5*x^4 - x^5 + E^(6*x)*(24 + 4*x - 4*x^2) + E^(4*x)*(72 + 48*x - 6*
x^2 - 6*x^3) + E^(2*x)*(96 + 112*x + 24*x^2 - 12*x^3 - 4*x^4) + (-112*x - 144*x^2 - 48*x^3 + 4*x^4 + 3*x^5 + E
^(8*x)*(-25*x + 8*x^2) + E^(6*x)*(-164*x - 24*x^2 + 24*x^3) + E^(4*x)*(-384*x - 228*x^2 + 30*x^3 + 24*x^4) + E
^(2*x)*(-368*x - 368*x^2 - 60*x^3 + 32*x^4 + 8*x^5))*Log[x] + (54*x - 36*x^2 + 6*x^3)*Log[x]^2)/((27*x - 18*x^
2 + 3*x^3)*Log[x]^2),x]

[Out]

2*x - 12*Defer[Int][E^(2*x)/Log[x]^2, x] - 2*Defer[Int][E^(4*x)/Log[x]^2, x] - (500*Defer[Int][E^(2*x)/((-3 +
x)*Log[x]^2), x])/9 - (50*Defer[Int][E^(4*x)/((-3 + x)*Log[x]^2), x])/3 - (20*Defer[Int][E^(6*x)/((-3 + x)*Log
[x]^2), x])/9 - Defer[Int][E^(8*x)/((-3 + x)*Log[x]^2), x]/9 + (32*Defer[Int][E^(2*x)/(x*Log[x]^2), x])/9 + (8
*Defer[Int][E^(4*x)/(x*Log[x]^2), x])/3 + (8*Defer[Int][E^(6*x)/(x*Log[x]^2), x])/9 + Defer[Int][E^(8*x)/(x*Lo
g[x]^2), x]/9 - (4*Defer[Int][(E^(2*x)*x)/Log[x]^2, x])/3 - Defer[Int][(2 + x)^4/((-3 + x)*x*Log[x]^2), x]/3 +
116*Defer[Int][E^(2*x)/Log[x], x] + 58*Defer[Int][E^(4*x)/Log[x], x] + 8*Defer[Int][E^(6*x)/Log[x], x] - (112
*Defer[Int][1/((-3 + x)^2*Log[x]), x])/3 - (500*Defer[Int][E^(2*x)/((-3 + x)^2*Log[x]), x])/3 - 50*Defer[Int][
E^(4*x)/((-3 + x)^2*Log[x]), x] - (20*Defer[Int][E^(6*x)/((-3 + x)^2*Log[x]), x])/3 - Defer[Int][E^(8*x)/((-3
+ x)^2*Log[x]), x]/3 + (1000*Defer[Int][E^(2*x)/((-3 + x)*Log[x]), x])/3 + 200*Defer[Int][E^(4*x)/((-3 + x)*Lo
g[x]), x] + 40*Defer[Int][E^(6*x)/((-3 + x)*Log[x]), x] + (8*Defer[Int][E^(8*x)/((-3 + x)*Log[x]), x])/3 + (80
*Defer[Int][(E^(2*x)*x)/Log[x], x])/3 + 8*Defer[Int][(E^(4*x)*x)/Log[x], x] - 48*Defer[Int][x/((-3 + x)^2*Log[
x]), x] + (8*Defer[Int][(E^(2*x)*x^2)/Log[x], x])/3 - 16*Defer[Int][x^2/((-3 + x)^2*Log[x]), x] + (4*Defer[Int
][x^3/((-3 + x)^2*Log[x]), x])/3 + Defer[Int][x^4/((-3 + x)^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {48+e^{8 x} (3-x)+80 x+40 x^2-5 x^4-x^5+e^{6 x} \left (24+4 x-4 x^2\right )+e^{4 x} \left (72+48 x-6 x^2-6 x^3\right )+e^{2 x} \left (96+112 x+24 x^2-12 x^3-4 x^4\right )+\left (-112 x-144 x^2-48 x^3+4 x^4+3 x^5+e^{8 x} \left (-25 x+8 x^2\right )+e^{6 x} \left (-164 x-24 x^2+24 x^3\right )+e^{4 x} \left (-384 x-228 x^2+30 x^3+24 x^4\right )+e^{2 x} \left (-368 x-368 x^2-60 x^3+32 x^4+8 x^5\right )\right ) \log (x)+\left (54 x-36 x^2+6 x^3\right ) \log ^2(x)}{x \left (27-18 x+3 x^2\right ) \log ^2(x)} \, dx\\ &=\int \frac {48+e^{8 x} (3-x)+80 x+40 x^2-5 x^4-x^5+e^{6 x} \left (24+4 x-4 x^2\right )+e^{4 x} \left (72+48 x-6 x^2-6 x^3\right )+e^{2 x} \left (96+112 x+24 x^2-12 x^3-4 x^4\right )+\left (-112 x-144 x^2-48 x^3+4 x^4+3 x^5+e^{8 x} \left (-25 x+8 x^2\right )+e^{6 x} \left (-164 x-24 x^2+24 x^3\right )+e^{4 x} \left (-384 x-228 x^2+30 x^3+24 x^4\right )+e^{2 x} \left (-368 x-368 x^2-60 x^3+32 x^4+8 x^5\right )\right ) \log (x)+\left (54 x-36 x^2+6 x^3\right ) \log ^2(x)}{3 (-3+x)^2 x \log ^2(x)} \, dx\\ &=\frac {1}{3} \int \frac {48+e^{8 x} (3-x)+80 x+40 x^2-5 x^4-x^5+e^{6 x} \left (24+4 x-4 x^2\right )+e^{4 x} \left (72+48 x-6 x^2-6 x^3\right )+e^{2 x} \left (96+112 x+24 x^2-12 x^3-4 x^4\right )+\left (-112 x-144 x^2-48 x^3+4 x^4+3 x^5+e^{8 x} \left (-25 x+8 x^2\right )+e^{6 x} \left (-164 x-24 x^2+24 x^3\right )+e^{4 x} \left (-384 x-228 x^2+30 x^3+24 x^4\right )+e^{2 x} \left (-368 x-368 x^2-60 x^3+32 x^4+8 x^5\right )\right ) \log (x)+\left (54 x-36 x^2+6 x^3\right ) \log ^2(x)}{(-3+x)^2 x \log ^2(x)} \, dx\\ &=\frac {1}{3} \int \left (6-\frac {\left (2+e^{2 x}+x\right )^4}{(-3+x) x \log ^2(x)}+\frac {\left (2+e^{2 x}+x\right )^3 \left (-14+3 x+e^{2 x} (-25+8 x)\right )}{(-3+x)^2 \log (x)}\right ) \, dx\\ &=2 x-\frac {1}{3} \int \frac {\left (2+e^{2 x}+x\right )^4}{(-3+x) x \log ^2(x)} \, dx+\frac {1}{3} \int \frac {\left (2+e^{2 x}+x\right )^3 \left (-14+3 x+e^{2 x} (-25+8 x)\right )}{(-3+x)^2 \log (x)} \, dx\\ &=2 x-\frac {1}{3} \int \left (\frac {e^{8 x}}{(-3+x) x \log ^2(x)}+\frac {4 e^{6 x} (2+x)}{(-3+x) x \log ^2(x)}+\frac {6 e^{4 x} (2+x)^2}{(-3+x) x \log ^2(x)}+\frac {4 e^{2 x} (2+x)^3}{(-3+x) x \log ^2(x)}+\frac {(2+x)^4}{(-3+x) x \log ^2(x)}\right ) \, dx+\frac {1}{3} \int \left (-\frac {112}{(-3+x)^2 \log (x)}-\frac {144 x}{(-3+x)^2 \log (x)}-\frac {48 x^2}{(-3+x)^2 \log (x)}+\frac {4 x^3}{(-3+x)^2 \log (x)}+\frac {3 x^4}{(-3+x)^2 \log (x)}+\frac {e^{8 x} (-25+8 x)}{(-3+x)^2 \log (x)}+\frac {4 e^{2 x} (2+x)^2 \left (-23+2 x^2\right )}{(-3+x)^2 \log (x)}+\frac {4 e^{6 x} \left (-41-6 x+6 x^2\right )}{(-3+x)^2 \log (x)}+\frac {6 e^{4 x} \left (-64-38 x+5 x^2+4 x^3\right )}{(-3+x)^2 \log (x)}\right ) \, dx\\ &=2 x-\frac {1}{3} \int \frac {e^{8 x}}{(-3+x) x \log ^2(x)} \, dx-\frac {1}{3} \int \frac {(2+x)^4}{(-3+x) x \log ^2(x)} \, dx+\frac {1}{3} \int \frac {e^{8 x} (-25+8 x)}{(-3+x)^2 \log (x)} \, dx-\frac {4}{3} \int \frac {e^{6 x} (2+x)}{(-3+x) x \log ^2(x)} \, dx-\frac {4}{3} \int \frac {e^{2 x} (2+x)^3}{(-3+x) x \log ^2(x)} \, dx+\frac {4}{3} \int \frac {x^3}{(-3+x)^2 \log (x)} \, dx+\frac {4}{3} \int \frac {e^{2 x} (2+x)^2 \left (-23+2 x^2\right )}{(-3+x)^2 \log (x)} \, dx+\frac {4}{3} \int \frac {e^{6 x} \left (-41-6 x+6 x^2\right )}{(-3+x)^2 \log (x)} \, dx-2 \int \frac {e^{4 x} (2+x)^2}{(-3+x) x \log ^2(x)} \, dx+2 \int \frac {e^{4 x} \left (-64-38 x+5 x^2+4 x^3\right )}{(-3+x)^2 \log (x)} \, dx-16 \int \frac {x^2}{(-3+x)^2 \log (x)} \, dx-\frac {112}{3} \int \frac {1}{(-3+x)^2 \log (x)} \, dx-48 \int \frac {x}{(-3+x)^2 \log (x)} \, dx+\int \frac {x^4}{(-3+x)^2 \log (x)} \, dx\\ &=2 x-\frac {1}{3} \int \left (\frac {e^{8 x}}{3 (-3+x) \log ^2(x)}-\frac {e^{8 x}}{3 x \log ^2(x)}\right ) \, dx+\frac {1}{3} \int \left (-\frac {e^{8 x}}{(-3+x)^2 \log (x)}+\frac {8 e^{8 x}}{(-3+x) \log (x)}\right ) \, dx-\frac {1}{3} \int \frac {(2+x)^4}{(-3+x) x \log ^2(x)} \, dx-\frac {4}{3} \int \left (\frac {5 e^{6 x}}{3 (-3+x) \log ^2(x)}-\frac {2 e^{6 x}}{3 x \log ^2(x)}\right ) \, dx-\frac {4}{3} \int \left (\frac {9 e^{2 x}}{\log ^2(x)}+\frac {125 e^{2 x}}{3 (-3+x) \log ^2(x)}-\frac {8 e^{2 x}}{3 x \log ^2(x)}+\frac {e^{2 x} x}{\log ^2(x)}\right ) \, dx+\frac {4}{3} \int \left (\frac {6 e^{6 x}}{\log (x)}-\frac {5 e^{6 x}}{(-3+x)^2 \log (x)}+\frac {30 e^{6 x}}{(-3+x) \log (x)}\right ) \, dx+\frac {4}{3} \int \left (\frac {87 e^{2 x}}{\log (x)}-\frac {125 e^{2 x}}{(-3+x)^2 \log (x)}+\frac {250 e^{2 x}}{(-3+x) \log (x)}+\frac {20 e^{2 x} x}{\log (x)}+\frac {2 e^{2 x} x^2}{\log (x)}\right ) \, dx+\frac {4}{3} \int \frac {x^3}{(-3+x)^2 \log (x)} \, dx-2 \int \left (\frac {e^{4 x}}{\log ^2(x)}+\frac {25 e^{4 x}}{3 (-3+x) \log ^2(x)}-\frac {4 e^{4 x}}{3 x \log ^2(x)}\right ) \, dx+2 \int \left (\frac {29 e^{4 x}}{\log (x)}-\frac {25 e^{4 x}}{(-3+x)^2 \log (x)}+\frac {100 e^{4 x}}{(-3+x) \log (x)}+\frac {4 e^{4 x} x}{\log (x)}\right ) \, dx-16 \int \frac {x^2}{(-3+x)^2 \log (x)} \, dx-\frac {112}{3} \int \frac {1}{(-3+x)^2 \log (x)} \, dx-48 \int \frac {x}{(-3+x)^2 \log (x)} \, dx+\int \frac {x^4}{(-3+x)^2 \log (x)} \, dx\\ &=2 x-\frac {1}{9} \int \frac {e^{8 x}}{(-3+x) \log ^2(x)} \, dx+\frac {1}{9} \int \frac {e^{8 x}}{x \log ^2(x)} \, dx-\frac {1}{3} \int \frac {(2+x)^4}{(-3+x) x \log ^2(x)} \, dx-\frac {1}{3} \int \frac {e^{8 x}}{(-3+x)^2 \log (x)} \, dx+\frac {8}{9} \int \frac {e^{6 x}}{x \log ^2(x)} \, dx-\frac {4}{3} \int \frac {e^{2 x} x}{\log ^2(x)} \, dx+\frac {4}{3} \int \frac {x^3}{(-3+x)^2 \log (x)} \, dx-2 \int \frac {e^{4 x}}{\log ^2(x)} \, dx-\frac {20}{9} \int \frac {e^{6 x}}{(-3+x) \log ^2(x)} \, dx+\frac {8}{3} \int \frac {e^{4 x}}{x \log ^2(x)} \, dx+\frac {8}{3} \int \frac {e^{8 x}}{(-3+x) \log (x)} \, dx+\frac {8}{3} \int \frac {e^{2 x} x^2}{\log (x)} \, dx+\frac {32}{9} \int \frac {e^{2 x}}{x \log ^2(x)} \, dx-\frac {20}{3} \int \frac {e^{6 x}}{(-3+x)^2 \log (x)} \, dx+8 \int \frac {e^{6 x}}{\log (x)} \, dx+8 \int \frac {e^{4 x} x}{\log (x)} \, dx-12 \int \frac {e^{2 x}}{\log ^2(x)} \, dx-16 \int \frac {x^2}{(-3+x)^2 \log (x)} \, dx-\frac {50}{3} \int \frac {e^{4 x}}{(-3+x) \log ^2(x)} \, dx+\frac {80}{3} \int \frac {e^{2 x} x}{\log (x)} \, dx-\frac {112}{3} \int \frac {1}{(-3+x)^2 \log (x)} \, dx+40 \int \frac {e^{6 x}}{(-3+x) \log (x)} \, dx-48 \int \frac {x}{(-3+x)^2 \log (x)} \, dx-50 \int \frac {e^{4 x}}{(-3+x)^2 \log (x)} \, dx-\frac {500}{9} \int \frac {e^{2 x}}{(-3+x) \log ^2(x)} \, dx+58 \int \frac {e^{4 x}}{\log (x)} \, dx+116 \int \frac {e^{2 x}}{\log (x)} \, dx-\frac {500}{3} \int \frac {e^{2 x}}{(-3+x)^2 \log (x)} \, dx+200 \int \frac {e^{4 x}}{(-3+x) \log (x)} \, dx+\frac {1000}{3} \int \frac {e^{2 x}}{(-3+x) \log (x)} \, dx+\int \frac {x^4}{(-3+x)^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.08, size = 28, normalized size = 0.97 \begin {gather*} \frac {1}{3} \left (6 x+\frac {\left (2+e^{2 x}+x\right )^4}{(-3+x) \log (x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(48 + E^(8*x)*(3 - x) + 80*x + 40*x^2 - 5*x^4 - x^5 + E^(6*x)*(24 + 4*x - 4*x^2) + E^(4*x)*(72 + 48*
x - 6*x^2 - 6*x^3) + E^(2*x)*(96 + 112*x + 24*x^2 - 12*x^3 - 4*x^4) + (-112*x - 144*x^2 - 48*x^3 + 4*x^4 + 3*x
^5 + E^(8*x)*(-25*x + 8*x^2) + E^(6*x)*(-164*x - 24*x^2 + 24*x^3) + E^(4*x)*(-384*x - 228*x^2 + 30*x^3 + 24*x^
4) + E^(2*x)*(-368*x - 368*x^2 - 60*x^3 + 32*x^4 + 8*x^5))*Log[x] + (54*x - 36*x^2 + 6*x^3)*Log[x]^2)/((27*x -
18*x^2 + 3*x^3)*Log[x]^2),x]

[Out]

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

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fricas [B]  time = 0.69, size = 86, normalized size = 2.97 \begin {gather*} \frac {x^{4} + 8 \, x^{3} + 24 \, x^{2} + 4 \, {\left (x + 2\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{2} + 4 \, x + 4\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{3} + 6 \, x^{2} + 12 \, x + 8\right )} e^{\left (2 \, x\right )} + 6 \, {\left (x^{2} - 3 \, x\right )} \log \relax (x) + 32 \, x + e^{\left (8 \, x\right )} + 16}{3 \, {\left (x - 3\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^3-36*x^2+54*x)*log(x)^2+((8*x^2-25*x)*exp(2*x)^4+(24*x^3-24*x^2-164*x)*exp(2*x)^3+(24*x^4+30*x
^3-228*x^2-384*x)*exp(2*x)^2+(8*x^5+32*x^4-60*x^3-368*x^2-368*x)*exp(2*x)+3*x^5+4*x^4-48*x^3-144*x^2-112*x)*lo
g(x)+(3-x)*exp(2*x)^4+(-4*x^2+4*x+24)*exp(2*x)^3+(-6*x^3-6*x^2+48*x+72)*exp(2*x)^2+(-4*x^4-12*x^3+24*x^2+112*x
+96)*exp(2*x)-x^5-5*x^4+40*x^2+80*x+48)/(3*x^3-18*x^2+27*x)/log(x)^2,x, algorithm="fricas")

[Out]

1/3*(x^4 + 8*x^3 + 24*x^2 + 4*(x + 2)*e^(6*x) + 6*(x^2 + 4*x + 4)*e^(4*x) + 4*(x^3 + 6*x^2 + 12*x + 8)*e^(2*x)
+ 6*(x^2 - 3*x)*log(x) + 32*x + e^(8*x) + 16)/((x - 3)*log(x))

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giac [B]  time = 0.25, size = 113, normalized size = 3.90 \begin {gather*} \frac {x^{4} + 4 \, x^{3} e^{\left (2 \, x\right )} + 8 \, x^{3} + 6 \, x^{2} e^{\left (4 \, x\right )} + 24 \, x^{2} e^{\left (2 \, x\right )} + 6 \, x^{2} \log \relax (x) + 24 \, x^{2} + 4 \, x e^{\left (6 \, x\right )} + 24 \, x e^{\left (4 \, x\right )} + 48 \, x e^{\left (2 \, x\right )} - 18 \, x \log \relax (x) + 32 \, x + e^{\left (8 \, x\right )} + 8 \, e^{\left (6 \, x\right )} + 24 \, e^{\left (4 \, x\right )} + 32 \, e^{\left (2 \, x\right )} + 16}{3 \, {\left (x \log \relax (x) - 3 \, \log \relax (x)\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^3-36*x^2+54*x)*log(x)^2+((8*x^2-25*x)*exp(2*x)^4+(24*x^3-24*x^2-164*x)*exp(2*x)^3+(24*x^4+30*x
^3-228*x^2-384*x)*exp(2*x)^2+(8*x^5+32*x^4-60*x^3-368*x^2-368*x)*exp(2*x)+3*x^5+4*x^4-48*x^3-144*x^2-112*x)*lo
g(x)+(3-x)*exp(2*x)^4+(-4*x^2+4*x+24)*exp(2*x)^3+(-6*x^3-6*x^2+48*x+72)*exp(2*x)^2+(-4*x^4-12*x^3+24*x^2+112*x
+96)*exp(2*x)-x^5-5*x^4+40*x^2+80*x+48)/(3*x^3-18*x^2+27*x)/log(x)^2,x, algorithm="giac")

[Out]

1/3*(x^4 + 4*x^3*e^(2*x) + 8*x^3 + 6*x^2*e^(4*x) + 24*x^2*e^(2*x) + 6*x^2*log(x) + 24*x^2 + 4*x*e^(6*x) + 24*x
*e^(4*x) + 48*x*e^(2*x) - 18*x*log(x) + 32*x + e^(8*x) + 8*e^(6*x) + 24*e^(4*x) + 32*e^(2*x) + 16)/(x*log(x) -
3*log(x))

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maple [B]  time = 0.07, size = 104, normalized size = 3.59

method	result	size
risch	\(2 x +\frac {x^{4}+4 \,{\mathrm e}^{2 x} x^{3}+6 x^{2} {\mathrm e}^{4 x}+4 x \,{\mathrm e}^{6 x}+{\mathrm e}^{8 x}+8 x^{3}+24 \,{\mathrm e}^{2 x} x^{2}+24 x \,{\mathrm e}^{4 x}+8 \,{\mathrm e}^{6 x}+24 x^{2}+48 x \,{\mathrm e}^{2 x}+24 \,{\mathrm e}^{4 x}+32 x +32 \,{\mathrm e}^{2 x}+16}{3 \left (x -3\right ) \ln \relax (x )}\)	\(104\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6*x^3-36*x^2+54*x)*ln(x)^2+((8*x^2-25*x)*exp(2*x)^4+(24*x^3-24*x^2-164*x)*exp(2*x)^3+(24*x^4+30*x^3-228*
x^2-384*x)*exp(2*x)^2+(8*x^5+32*x^4-60*x^3-368*x^2-368*x)*exp(2*x)+3*x^5+4*x^4-48*x^3-144*x^2-112*x)*ln(x)+(3-
x)*exp(2*x)^4+(-4*x^2+4*x+24)*exp(2*x)^3+(-6*x^3-6*x^2+48*x+72)*exp(2*x)^2+(-4*x^4-12*x^3+24*x^2+112*x+96)*exp
(2*x)-x^5-5*x^4+40*x^2+80*x+48)/(3*x^3-18*x^2+27*x)/ln(x)^2,x,method=_RETURNVERBOSE)

[Out]

2*x+1/3*(x^4+4*exp(2*x)*x^3+6*x^2*exp(4*x)+4*x*exp(6*x)+exp(8*x)+8*x^3+24*exp(2*x)*x^2+24*x*exp(4*x)+8*exp(6*x
)+24*x^2+48*x*exp(2*x)+24*exp(4*x)+32*x+32*exp(2*x)+16)/(x-3)/ln(x)

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maxima [B]  time = 0.42, size = 86, normalized size = 2.97 \begin {gather*} \frac {x^{4} + 8 \, x^{3} + 24 \, x^{2} + 4 \, {\left (x + 2\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{2} + 4 \, x + 4\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{3} + 6 \, x^{2} + 12 \, x + 8\right )} e^{\left (2 \, x\right )} + 6 \, {\left (x^{2} - 3 \, x\right )} \log \relax (x) + 32 \, x + e^{\left (8 \, x\right )} + 16}{3 \, {\left (x - 3\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^3-36*x^2+54*x)*log(x)^2+((8*x^2-25*x)*exp(2*x)^4+(24*x^3-24*x^2-164*x)*exp(2*x)^3+(24*x^4+30*x
^3-228*x^2-384*x)*exp(2*x)^2+(8*x^5+32*x^4-60*x^3-368*x^2-368*x)*exp(2*x)+3*x^5+4*x^4-48*x^3-144*x^2-112*x)*lo
g(x)+(3-x)*exp(2*x)^4+(-4*x^2+4*x+24)*exp(2*x)^3+(-6*x^3-6*x^2+48*x+72)*exp(2*x)^2+(-4*x^4-12*x^3+24*x^2+112*x
+96)*exp(2*x)-x^5-5*x^4+40*x^2+80*x+48)/(3*x^3-18*x^2+27*x)/log(x)^2,x, algorithm="maxima")

[Out]

1/3*(x^4 + 8*x^3 + 24*x^2 + 4*(x + 2)*e^(6*x) + 6*(x^2 + 4*x + 4)*e^(4*x) + 4*(x^3 + 6*x^2 + 12*x + 8)*e^(2*x)
+ 6*(x^2 - 3*x)*log(x) + 32*x + e^(8*x) + 16)/((x - 3)*log(x))

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mupad [B]  time = 2.56, size = 217, normalized size = 7.48 \begin {gather*} 21\,x-\frac {625\,x}{3\,\left (x^2-6\,x+9\right )}+\frac {\frac {{\left (x+{\mathrm {e}}^{2\,x}+2\right )}^4}{3\,\left (x-3\right )}-\frac {x\,\ln \relax (x)\,{\left (x+{\mathrm {e}}^{2\,x}+2\right )}^3\,\left (3\,x-25\,{\mathrm {e}}^{2\,x}+8\,x\,{\mathrm {e}}^{2\,x}-14\right )}{3\,{\left (x-3\right )}^2}}{\ln \relax (x)}+\frac {22\,x^2}{3}+x^3-\frac {{\mathrm {e}}^{2\,x}\,\left (-\frac {8\,x^5}{3}-\frac {32\,x^4}{3}+20\,x^3+\frac {368\,x^2}{3}+\frac {368\,x}{3}\right )}{x^2-6\,x+9}-\frac {{\mathrm {e}}^{8\,x}\,\left (\frac {25\,x}{3}-\frac {8\,x^2}{3}\right )}{x^2-6\,x+9}-\frac {{\mathrm {e}}^{6\,x}\,\left (-8\,x^3+8\,x^2+\frac {164\,x}{3}\right )}{x^2-6\,x+9}-\frac {{\mathrm {e}}^{4\,x}\,\left (-8\,x^4-10\,x^3+76\,x^2+128\,x\right )}{x^2-6\,x+9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((80*x + exp(6*x)*(4*x - 4*x^2 + 24) + exp(4*x)*(48*x - 6*x^2 - 6*x^3 + 72) + log(x)^2*(54*x - 36*x^2 + 6*x
^3) - exp(8*x)*(x - 3) + exp(2*x)*(112*x + 24*x^2 - 12*x^3 - 4*x^4 + 96) - log(x)*(112*x + exp(8*x)*(25*x - 8*
x^2) + exp(6*x)*(164*x + 24*x^2 - 24*x^3) + exp(4*x)*(384*x + 228*x^2 - 30*x^3 - 24*x^4) + exp(2*x)*(368*x + 3
68*x^2 + 60*x^3 - 32*x^4 - 8*x^5) + 144*x^2 + 48*x^3 - 4*x^4 - 3*x^5) + 40*x^2 - 5*x^4 - x^5 + 48)/(log(x)^2*(
27*x - 18*x^2 + 3*x^3)),x)

[Out]

21*x - (625*x)/(3*(x^2 - 6*x + 9)) + ((x + exp(2*x) + 2)^4/(3*(x - 3)) - (x*log(x)*(x + exp(2*x) + 2)^3*(3*x -
25*exp(2*x) + 8*x*exp(2*x) - 14))/(3*(x - 3)^2))/log(x) + (22*x^2)/3 + x^3 - (exp(2*x)*((368*x)/3 + (368*x^2)
/3 + 20*x^3 - (32*x^4)/3 - (8*x^5)/3))/(x^2 - 6*x + 9) - (exp(8*x)*((25*x)/3 - (8*x^2)/3))/(x^2 - 6*x + 9) - (
exp(6*x)*((164*x)/3 + 8*x^2 - 8*x^3))/(x^2 - 6*x + 9) - (exp(4*x)*(128*x + 76*x^2 - 10*x^3 - 8*x^4))/(x^2 - 6*
x + 9)

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sympy [B]  time = 0.71, size = 291, normalized size = 10.03 \begin {gather*} 2 x + \frac {\left (9 x^{3} \log {\relax (x )}^{3} - 81 x^{2} \log {\relax (x )}^{3} + 243 x \log {\relax (x )}^{3} - 243 \log {\relax (x )}^{3}\right ) e^{8 x} + \left (36 x^{4} \log {\relax (x )}^{3} - 252 x^{3} \log {\relax (x )}^{3} + 324 x^{2} \log {\relax (x )}^{3} + 972 x \log {\relax (x )}^{3} - 1944 \log {\relax (x )}^{3}\right ) e^{6 x} + \left (54 x^{5} \log {\relax (x )}^{3} - 270 x^{4} \log {\relax (x )}^{3} - 270 x^{3} \log {\relax (x )}^{3} + 2430 x^{2} \log {\relax (x )}^{3} - 5832 \log {\relax (x )}^{3}\right ) e^{4 x} + \left (36 x^{6} \log {\relax (x )}^{3} - 108 x^{5} \log {\relax (x )}^{3} - 540 x^{4} \log {\relax (x )}^{3} + 1260 x^{3} \log {\relax (x )}^{3} + 3240 x^{2} \log {\relax (x )}^{3} - 3888 x \log {\relax (x )}^{3} - 7776 \log {\relax (x )}^{3}\right ) e^{2 x}}{27 x^{4} \log {\relax (x )}^{4} - 324 x^{3} \log {\relax (x )}^{4} + 1458 x^{2} \log {\relax (x )}^{4} - 2916 x \log {\relax (x )}^{4} + 2187 \log {\relax (x )}^{4}} + \frac {x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16}{\left (3 x - 9\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x**3-36*x**2+54*x)*ln(x)**2+((8*x**2-25*x)*exp(2*x)**4+(24*x**3-24*x**2-164*x)*exp(2*x)**3+(24*x
**4+30*x**3-228*x**2-384*x)*exp(2*x)**2+(8*x**5+32*x**4-60*x**3-368*x**2-368*x)*exp(2*x)+3*x**5+4*x**4-48*x**3
-144*x**2-112*x)*ln(x)+(3-x)*exp(2*x)**4+(-4*x**2+4*x+24)*exp(2*x)**3+(-6*x**3-6*x**2+48*x+72)*exp(2*x)**2+(-4
*x**4-12*x**3+24*x**2+112*x+96)*exp(2*x)-x**5-5*x**4+40*x**2+80*x+48)/(3*x**3-18*x**2+27*x)/ln(x)**2,x)

[Out]

2*x + ((9*x**3*log(x)**3 - 81*x**2*log(x)**3 + 243*x*log(x)**3 - 243*log(x)**3)*exp(8*x) + (36*x**4*log(x)**3
- 252*x**3*log(x)**3 + 324*x**2*log(x)**3 + 972*x*log(x)**3 - 1944*log(x)**3)*exp(6*x) + (54*x**5*log(x)**3 -
270*x**4*log(x)**3 - 270*x**3*log(x)**3 + 2430*x**2*log(x)**3 - 5832*log(x)**3)*exp(4*x) + (36*x**6*log(x)**3
- 108*x**5*log(x)**3 - 540*x**4*log(x)**3 + 1260*x**3*log(x)**3 + 3240*x**2*log(x)**3 - 3888*x*log(x)**3 - 777
6*log(x)**3)*exp(2*x))/(27*x**4*log(x)**4 - 324*x**3*log(x)**4 + 1458*x**2*log(x)**4 - 2916*x*log(x)**4 + 2187
*log(x)**4) + (x**4 + 8*x**3 + 24*x**2 + 32*x + 16)/((3*x - 9)*log(x))

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