3.91.86 \(\int \frac {e^x (-90+180 x-1090 x^2+2165 x^3-1835 x^4+580 x^5-10 x^6-10 x^7+5 x^8)+e^x (45-60 x+165 x^2-300 x^3+150 x^4+75 x^5-105 x^6+30 x^7) \log (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12})+e^x (45-90 x+225 x^2-450 x^3+450 x^4-225 x^5+45 x^6) \log ^2(x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12})}{-9 x^2+3 x^3-31 x^4+31 x^5-4 x^6-9 x^7+2 x^8+x^9+(-18 x^2+12 x^3-66 x^4+84 x^5-36 x^6-6 x^7+6 x^8) \log (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12})+(-9 x^2+9 x^3-36 x^4+54 x^5-36 x^6+9 x^7) \log ^2(x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12})} \, dx\)

Optimal. Leaf size=39 \[ -4+\frac {5 e^x}{x+\frac {x}{\frac {x}{3}+\log \left (\left (-x+(1-x)^4 x^2\right )^2\right )}} \]

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Rubi [F]  time = 27.85, 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 {e^x \left (-90+180 x-1090 x^2+2165 x^3-1835 x^4+580 x^5-10 x^6-10 x^7+5 x^8\right )+e^x \left (45-60 x+165 x^2-300 x^3+150 x^4+75 x^5-105 x^6+30 x^7\right ) \log \left (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12}\right )+e^x \left (45-90 x+225 x^2-450 x^3+450 x^4-225 x^5+45 x^6\right ) \log ^2\left (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12}\right )}{-9 x^2+3 x^3-31 x^4+31 x^5-4 x^6-9 x^7+2 x^8+x^9+\left (-18 x^2+12 x^3-66 x^4+84 x^5-36 x^6-6 x^7+6 x^8\right ) \log \left (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12}\right )+\left (-9 x^2+9 x^3-36 x^4+54 x^5-36 x^6+9 x^7\right ) \log ^2\left (x^2-2 x^3+9 x^4-20 x^5+36 x^6-58 x^7+70 x^8-56 x^9+28 x^{10}-8 x^{11}+x^{12}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(-90 + 180*x - 1090*x^2 + 2165*x^3 - 1835*x^4 + 580*x^5 - 10*x^6 - 10*x^7 + 5*x^8) + E^x*(45 - 60*x +
165*x^2 - 300*x^3 + 150*x^4 + 75*x^5 - 105*x^6 + 30*x^7)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 +
70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12] + E^x*(45 - 90*x + 225*x^2 - 450*x^3 + 450*x^4 - 225*x^5 + 45*x^6)
*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12]^2)/(-9*x^2 +
3*x^3 - 31*x^4 + 31*x^5 - 4*x^6 - 9*x^7 + 2*x^8 + x^9 + (-18*x^2 + 12*x^3 - 66*x^4 + 84*x^5 - 36*x^6 - 6*x^7 +
6*x^8)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12] + (-9*
x^2 + 9*x^3 - 36*x^4 + 54*x^5 - 36*x^6 + 9*x^7)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 -
56*x^9 + 28*x^10 - 8*x^11 + x^12]^2),x]

[Out]

(5*E^x)/x + 90*Defer[Int][E^x/(x^2*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] - 75*D
efer[Int][E^x/(x*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] - 630*Defer[Int][E^x/((-
1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] + 12
60*Defer[Int][(E^x*x)/((-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x
^4 + x^5)^2])^2), x] - 900*Defer[Int][(E^x*x^2)/((-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)*(3 + x + 3*Log[x^2*(-1
+ x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] + 90*Defer[Int][(E^x*x^3)/((-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^
5)*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] + 90*Defer[Int][(E^x*x^4)/((-1 + x - 4
*x^2 + 6*x^3 - 4*x^4 + x^5)*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])^2), x] + 15*Defer[In
t][E^x/(x^2*(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])), x] - 15*Defer[Int][E^x/(x*(3 + x +
3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 e^x \left (18-36 x+218 x^2-433 x^3+367 x^4-116 x^5+2 x^6+2 x^7-x^8-3 \left (3-4 x+11 x^2-20 x^3+10 x^4+5 x^5-7 x^6+2 x^7\right ) \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )-9 \left (1-2 x+5 x^2-10 x^3+10 x^4-5 x^5+x^6\right ) \log ^2\left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )}{x^2 \left (1-x+4 x^2-6 x^3+4 x^4-x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^x \left (18-36 x+218 x^2-433 x^3+367 x^4-116 x^5+2 x^6+2 x^7-x^8-3 \left (3-4 x+11 x^2-20 x^3+10 x^4+5 x^5-7 x^6+2 x^7\right ) \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )-9 \left (1-2 x+5 x^2-10 x^3+10 x^4-5 x^5+x^6\right ) \log ^2\left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )}{x^2 \left (1-x+4 x^2-6 x^3+4 x^4-x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx\\ &=5 \int \left (\frac {e^x (-1+x)}{x^2}+\frac {3 e^x \left (-6+11 x-71 x^2+140 x^3-114 x^4+32 x^5+x^6\right )}{x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}-\frac {3 e^x (-1+x)}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )}\right ) \, dx\\ &=5 \int \frac {e^x (-1+x)}{x^2} \, dx+15 \int \frac {e^x \left (-6+11 x-71 x^2+140 x^3-114 x^4+32 x^5+x^6\right )}{x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx-15 \int \frac {e^x (-1+x)}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx\\ &=\frac {5 e^x}{x}+15 \int \left (\frac {6 e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}-\frac {5 e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}+\frac {6 e^x \left (-7+14 x-10 x^2+x^3+x^4\right )}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}\right ) \, dx-15 \int \left (-\frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )}+\frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )}\right ) \, dx\\ &=\frac {5 e^x}{x}+15 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-15 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-75 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x \left (-7+14 x-10 x^2+x^3+x^4\right )}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx\\ &=\frac {5 e^x}{x}+15 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-15 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-75 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \left (-\frac {7 e^x}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}+\frac {14 e^x x}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}-\frac {10 e^x x^2}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}+\frac {e^x x^3}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}+\frac {e^x x^4}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2}\right ) \, dx\\ &=\frac {5 e^x}{x}+15 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-15 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )} \, dx-75 \int \frac {e^x}{x \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x}{x^2 \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x x^3}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+90 \int \frac {e^x x^4}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx-630 \int \frac {e^x}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx-900 \int \frac {e^x x^2}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx+1260 \int \frac {e^x x}{\left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right ) \left (3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 47, normalized size = 1.21 \begin {gather*} \frac {5 e^x \left (1-\frac {3}{3+x+3 \log \left (x^2 \left (-1+x-4 x^2+6 x^3-4 x^4+x^5\right )^2\right )}\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(-90 + 180*x - 1090*x^2 + 2165*x^3 - 1835*x^4 + 580*x^5 - 10*x^6 - 10*x^7 + 5*x^8) + E^x*(45 -
60*x + 165*x^2 - 300*x^3 + 150*x^4 + 75*x^5 - 105*x^6 + 30*x^7)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58
*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12] + E^x*(45 - 90*x + 225*x^2 - 450*x^3 + 450*x^4 - 225*x^5 + 4
5*x^6)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12]^2)/(-9*
x^2 + 3*x^3 - 31*x^4 + 31*x^5 - 4*x^6 - 9*x^7 + 2*x^8 + x^9 + (-18*x^2 + 12*x^3 - 66*x^4 + 84*x^5 - 36*x^6 - 6
*x^7 + 6*x^8)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12]
+ (-9*x^2 + 9*x^3 - 36*x^4 + 54*x^5 - 36*x^6 + 9*x^7)*Log[x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*
x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12]^2),x]

[Out]

(5*E^x*(1 - 3/(3 + x + 3*Log[x^2*(-1 + x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)^2])))/x

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fricas [B]  time = 1.17, size = 129, normalized size = 3.31 \begin {gather*} \frac {5 \, {\left (x e^{x} + 3 \, e^{x} \log \left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 58 \, x^{7} + 36 \, x^{6} - 20 \, x^{5} + 9 \, x^{4} - 2 \, x^{3} + x^{2}\right )\right )}}{x^{2} + 3 \, x \log \left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 58 \, x^{7} + 36 \, x^{6} - 20 \, x^{5} + 9 \, x^{4} - 2 \, x^{3} + x^{2}\right ) + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((45*x^6-225*x^5+450*x^4-450*x^3+225*x^2-90*x+45)*exp(x)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58*x^
7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(30*x^7-105*x^6+75*x^5+150*x^4-300*x^3+165*x^2-60*x+45)*exp(x)*log(x^12-8*x
^11+28*x^10-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+(5*x^8-10*x^7-10*x^6+580*x^5-1835*x^4+2165*x^3
-1090*x^2+180*x-90)*exp(x))/((9*x^7-36*x^6+54*x^5-36*x^4+9*x^3-9*x^2)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58
*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(6*x^8-6*x^7-36*x^6+84*x^5-66*x^4+12*x^3-18*x^2)*log(x^12-8*x^11+28*x^10
-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+x^9+2*x^8-9*x^7-4*x^6+31*x^5-31*x^4+3*x^3-9*x^2),x, algor
ithm="fricas")

[Out]

5*(x*e^x + 3*e^x*log(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 58*x^7 + 36*x^6 - 20*x^5 + 9*x^4 - 2*x^3 + x^
2))/(x^2 + 3*x*log(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 58*x^7 + 36*x^6 - 20*x^5 + 9*x^4 - 2*x^3 + x^2)
+ 3*x)

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giac [B]  time = 8.88, size = 129, normalized size = 3.31 \begin {gather*} \frac {5 \, {\left (x e^{x} + 3 \, e^{x} \log \left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 58 \, x^{7} + 36 \, x^{6} - 20 \, x^{5} + 9 \, x^{4} - 2 \, x^{3} + x^{2}\right )\right )}}{x^{2} + 3 \, x \log \left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 58 \, x^{7} + 36 \, x^{6} - 20 \, x^{5} + 9 \, x^{4} - 2 \, x^{3} + x^{2}\right ) + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((45*x^6-225*x^5+450*x^4-450*x^3+225*x^2-90*x+45)*exp(x)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58*x^
7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(30*x^7-105*x^6+75*x^5+150*x^4-300*x^3+165*x^2-60*x+45)*exp(x)*log(x^12-8*x
^11+28*x^10-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+(5*x^8-10*x^7-10*x^6+580*x^5-1835*x^4+2165*x^3
-1090*x^2+180*x-90)*exp(x))/((9*x^7-36*x^6+54*x^5-36*x^4+9*x^3-9*x^2)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58
*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(6*x^8-6*x^7-36*x^6+84*x^5-66*x^4+12*x^3-18*x^2)*log(x^12-8*x^11+28*x^10
-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+x^9+2*x^8-9*x^7-4*x^6+31*x^5-31*x^4+3*x^3-9*x^2),x, algor
ithm="giac")

[Out]

5*(x*e^x + 3*e^x*log(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 58*x^7 + 36*x^6 - 20*x^5 + 9*x^4 - 2*x^3 + x^
2))/(x^2 + 3*x*log(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 58*x^7 + 36*x^6 - 20*x^5 + 9*x^4 - 2*x^3 + x^2)
+ 3*x)

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maple [C]  time = 0.37, size = 454, normalized size = 11.64

method	result	size
risch	\(\frac {5 \,{\mathrm e}^{x}}{x}-\frac {30 i {\mathrm e}^{x}}{x \left (3 \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-6 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+3 \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+3 \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )-3 \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )^{2}+3 \pi \mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )-6 \pi \,\mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )\right ) \mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )^{2}+3 \pi \mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )^{3}-3 \pi \,\mathrm {csgn}\left (i \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right ) \mathrm {csgn}\left (i x^{2} \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )^{2}+3 \pi \mathrm {csgn}\left (i x^{2} \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )^{2}\right )^{3}+2 i x +12 i \ln \relax (x )+12 i \ln \left (x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+x -1\right )+6 i\right )}\)	\(454\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((45*x^6-225*x^5+450*x^4-450*x^3+225*x^2-90*x+45)*exp(x)*ln(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58*x^7+36*x^
6-20*x^5+9*x^4-2*x^3+x^2)^2+(30*x^7-105*x^6+75*x^5+150*x^4-300*x^3+165*x^2-60*x+45)*exp(x)*ln(x^12-8*x^11+28*x
^10-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+(5*x^8-10*x^7-10*x^6+580*x^5-1835*x^4+2165*x^3-1090*x^
2+180*x-90)*exp(x))/((9*x^7-36*x^6+54*x^5-36*x^4+9*x^3-9*x^2)*ln(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58*x^7+36*x
^6-20*x^5+9*x^4-2*x^3+x^2)^2+(6*x^8-6*x^7-36*x^6+84*x^5-66*x^4+12*x^3-18*x^2)*ln(x^12-8*x^11+28*x^10-56*x^9+70
*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+x^9+2*x^8-9*x^7-4*x^6+31*x^5-31*x^4+3*x^3-9*x^2),x,method=_RETURNVE
RBOSE)

[Out]

5*exp(x)/x-30*I*exp(x)/x/(3*Pi*csgn(I*x)^2*csgn(I*x^2)-6*Pi*csgn(I*x)*csgn(I*x^2)^2+3*Pi*csgn(I*x^2)^3+3*Pi*cs
gn(I*x^2)*csgn(I*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)*csgn(I*x^2*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)-3*Pi*csgn(I*x^2)*csg
n(I*x^2*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)^2+3*Pi*csgn(I*(x^5-4*x^4+6*x^3-4*x^2+x-1))^2*csgn(I*(x^5-4*x^4+6*x^3-4*
x^2+x-1)^2)-6*Pi*csgn(I*(x^5-4*x^4+6*x^3-4*x^2+x-1))*csgn(I*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)^2+3*Pi*csgn(I*(x^5-
4*x^4+6*x^3-4*x^2+x-1)^2)^3-3*Pi*csgn(I*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)*csgn(I*x^2*(x^5-4*x^4+6*x^3-4*x^2+x-1)^
2)^2+3*Pi*csgn(I*x^2*(x^5-4*x^4+6*x^3-4*x^2+x-1)^2)^3+2*I*x+12*I*ln(x)+12*I*ln(x^5-4*x^4+6*x^3-4*x^2+x-1)+6*I)

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maxima [B]  time = 0.45, size = 77, normalized size = 1.97 \begin {gather*} \frac {5 \, {\left ({\left (x + 6 \, \log \relax (x)\right )} e^{x} + 6 \, e^{x} \log \left (x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + x - 1\right )\right )}}{x^{2} + 6 \, x \log \left (x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + x - 1\right ) + 6 \, x \log \relax (x) + 3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((45*x^6-225*x^5+450*x^4-450*x^3+225*x^2-90*x+45)*exp(x)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58*x^
7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(30*x^7-105*x^6+75*x^5+150*x^4-300*x^3+165*x^2-60*x+45)*exp(x)*log(x^12-8*x
^11+28*x^10-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+(5*x^8-10*x^7-10*x^6+580*x^5-1835*x^4+2165*x^3
-1090*x^2+180*x-90)*exp(x))/((9*x^7-36*x^6+54*x^5-36*x^4+9*x^3-9*x^2)*log(x^12-8*x^11+28*x^10-56*x^9+70*x^8-58
*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)^2+(6*x^8-6*x^7-36*x^6+84*x^5-66*x^4+12*x^3-18*x^2)*log(x^12-8*x^11+28*x^10
-56*x^9+70*x^8-58*x^7+36*x^6-20*x^5+9*x^4-2*x^3+x^2)+x^9+2*x^8-9*x^7-4*x^6+31*x^5-31*x^4+3*x^3-9*x^2),x, algor
ithm="maxima")

[Out]

5*((x + 6*log(x))*e^x + 6*e^x*log(x^5 - 4*x^4 + 6*x^3 - 4*x^2 + x - 1))/(x^2 + 6*x*log(x^5 - 4*x^4 + 6*x^3 - 4
*x^2 + x - 1) + 6*x*log(x) + 3*x)

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mupad [B]  time = 8.76, size = 77, normalized size = 1.97 \begin {gather*} \frac {5\,{\mathrm {e}}^x}{x}-\frac {15\,{\mathrm {e}}^x}{3\,x+3\,x\,\ln \left (x^{12}-8\,x^{11}+28\,x^{10}-56\,x^9+70\,x^8-58\,x^7+36\,x^6-20\,x^5+9\,x^4-2\,x^3+x^2\right )+x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*log(x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12)*(
165*x^2 - 60*x - 300*x^3 + 150*x^4 + 75*x^5 - 105*x^6 + 30*x^7 + 45) - exp(x)*(1090*x^2 - 180*x - 2165*x^3 + 1
835*x^4 - 580*x^5 + 10*x^6 + 10*x^7 - 5*x^8 + 90) + exp(x)*log(x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7
+ 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12)^2*(225*x^2 - 90*x - 450*x^3 + 450*x^4 - 225*x^5 + 45*x^6 + 45))/(
log(x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 28*x^10 - 8*x^11 + x^12)*(18*x^2 - 12*x
^3 + 66*x^4 - 84*x^5 + 36*x^6 + 6*x^7 - 6*x^8) + log(x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 -
56*x^9 + 28*x^10 - 8*x^11 + x^12)^2*(9*x^2 - 9*x^3 + 36*x^4 - 54*x^5 + 36*x^6 - 9*x^7) + 9*x^2 - 3*x^3 + 31*x
^4 - 31*x^5 + 4*x^6 + 9*x^7 - 2*x^8 - x^9),x)

[Out]

(5*exp(x))/x - (15*exp(x))/(3*x + 3*x*log(x^2 - 2*x^3 + 9*x^4 - 20*x^5 + 36*x^6 - 58*x^7 + 70*x^8 - 56*x^9 + 2
8*x^10 - 8*x^11 + x^12) + x^2)

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sympy [B]  time = 0.99, size = 126, normalized size = 3.23 \begin {gather*} \frac {\left (5 x + 15 \log {\left (x^{12} - 8 x^{11} + 28 x^{10} - 56 x^{9} + 70 x^{8} - 58 x^{7} + 36 x^{6} - 20 x^{5} + 9 x^{4} - 2 x^{3} + x^{2} \right )}\right ) e^{x}}{x^{2} + 3 x \log {\left (x^{12} - 8 x^{11} + 28 x^{10} - 56 x^{9} + 70 x^{8} - 58 x^{7} + 36 x^{6} - 20 x^{5} + 9 x^{4} - 2 x^{3} + x^{2} \right )} + 3 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((45*x**6-225*x**5+450*x**4-450*x**3+225*x**2-90*x+45)*exp(x)*ln(x**12-8*x**11+28*x**10-56*x**9+70*x
**8-58*x**7+36*x**6-20*x**5+9*x**4-2*x**3+x**2)**2+(30*x**7-105*x**6+75*x**5+150*x**4-300*x**3+165*x**2-60*x+4
5)*exp(x)*ln(x**12-8*x**11+28*x**10-56*x**9+70*x**8-58*x**7+36*x**6-20*x**5+9*x**4-2*x**3+x**2)+(5*x**8-10*x**
7-10*x**6+580*x**5-1835*x**4+2165*x**3-1090*x**2+180*x-90)*exp(x))/((9*x**7-36*x**6+54*x**5-36*x**4+9*x**3-9*x
**2)*ln(x**12-8*x**11+28*x**10-56*x**9+70*x**8-58*x**7+36*x**6-20*x**5+9*x**4-2*x**3+x**2)**2+(6*x**8-6*x**7-3
6*x**6+84*x**5-66*x**4+12*x**3-18*x**2)*ln(x**12-8*x**11+28*x**10-56*x**9+70*x**8-58*x**7+36*x**6-20*x**5+9*x*
*4-2*x**3+x**2)+x**9+2*x**8-9*x**7-4*x**6+31*x**5-31*x**4+3*x**3-9*x**2),x)

[Out]

(5*x + 15*log(x**12 - 8*x**11 + 28*x**10 - 56*x**9 + 70*x**8 - 58*x**7 + 36*x**6 - 20*x**5 + 9*x**4 - 2*x**3 +
x**2))*exp(x)/(x**2 + 3*x*log(x**12 - 8*x**11 + 28*x**10 - 56*x**9 + 70*x**8 - 58*x**7 + 36*x**6 - 20*x**5 +
9*x**4 - 2*x**3 + x**2) + 3*x)

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