3.95.51 \(\int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} (-2 x^2-2 x^3+54 x^4+18 x^5)+e^5 (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6)+(144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} (2 x+6 x^2-162 x^3-54 x^4)+e^5 (34 x+120 x^2-1434 x^3-972 x^4-162 x^5)) \log (x)+(-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} (-4 x+162 x^2+54 x^3)+e^5 (-72 x+1440 x^2+972 x^3+162 x^4)) \log ^2(x)+(-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} (-54 x-18 x^2)+e^5 (-486 x-324 x^2-54 x^3)) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} (-27 x^3-9 x^4)+e^5 (-243 x^3-162 x^4-27 x^5)+(2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} (81 x^2+27 x^3)+e^5 (729 x^2+486 x^3+81 x^4)) \log (x)+(-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} (-81 x-27 x^2)+e^5 (-729 x-486 x^2-81 x^3)) \log ^2(x)+(729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 (243+162 x+27 x^2)) \log ^3(x)} \, dx\)

Optimal. Leaf size=28 \[ 2-\left (x+\frac {x}{\left (9+e^5+3 x\right ) (-x+\log (x))}\right )^2 \]

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Rubi [F]  time = 5.27, 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 {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(18*x - 156*x^2 - 276*x^3 + 1386*x^4 + 2*E^15*x^4 + 1458*x^5 + 486*x^6 + 54*x^7 + E^10*(-2*x^2 - 2*x^3 + 5
4*x^4 + 18*x^5) + E^5*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) + (144*x + 594*x^2 - 4140*x^3 - 6*E
^15*x^3 - 4356*x^4 - 1458*x^5 - 162*x^6 + E^10*(2*x + 6*x^2 - 162*x^3 - 54*x^4) + E^5*(34*x + 120*x^2 - 1434*x
^3 - 972*x^4 - 162*x^5))*Log[x] + (-324*x + 4212*x^2 + 6*E^15*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5 + E^10*(-4*x
+ 162*x^2 + 54*x^3) + E^5*(-72*x + 1440*x^2 + 972*x^3 + 162*x^4))*Log[x]^2 + (-1458*x - 2*E^15*x - 1458*x^2 -
486*x^3 - 54*x^4 + E^10*(-54*x - 18*x^2) + E^5*(-486*x - 324*x^2 - 54*x^3))*Log[x]^3)/(-729*x^3 - E^15*x^3 -
729*x^4 - 243*x^5 - 27*x^6 + E^10*(-27*x^3 - 9*x^4) + E^5*(-243*x^3 - 162*x^4 - 27*x^5) + (2187*x^2 + 3*E^15*x
^2 + 2187*x^3 + 729*x^4 + 81*x^5 + E^10*(81*x^2 + 27*x^3) + E^5*(729*x^2 + 486*x^3 + 81*x^4))*Log[x] + (-2187*
x - 3*E^15*x - 2187*x^2 - 729*x^3 - 81*x^4 + E^10*(-81*x - 27*x^2) + E^5*(-729*x - 486*x^2 - 81*x^3))*Log[x]^2
+ (729 + E^15 + 729*x + 243*x^2 + 27*x^3 + E^10*(27 + 9*x) + E^5*(243 + 162*x + 27*x^2))*Log[x]^3),x]

[Out]

-x^2 + (2*Defer[Int][(x - Log[x])^(-3), x])/9 + (2*(108 + 21*E^5 + E^10)*Defer[Int][1/((9 + E^5 + 3*x)^2*(x -
Log[x])^3), x])/9 - (2*(21 + 2*E^5)*Defer[Int][1/((9 + E^5 + 3*x)*(x - Log[x])^3), x])/9 + (2*(12 + E^5)*Defer
[Int][(x - Log[x])^(-2), x])/9 - (2*Defer[Int][x/(x - Log[x])^2, x])/3 + (2*(9 + E^5)^2*Defer[Int][1/((9 + E^5
+ 3*x)^3*(x - Log[x])^2), x])/3 - (2*(9 + E^5)*Defer[Int][1/((9 + E^5 + 3*x)^2*(x - Log[x])^2), x])/3 - (2*(1
08 + 21*E^5 + E^10)*Defer[Int][1/((9 + E^5 + 3*x)*(x - Log[x])^2), x])/9 + (2*Defer[Int][(x - Log[x])^(-1), x]
)/3 - (2*(9 + E^5)^2*Defer[Int][1/((9 + E^5 + 3*x)^2*(x - Log[x])), x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{\left (-729-e^{15}\right ) x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx\\ &=\int \frac {18 x-156 x^2-276 x^3+\left (1386+2 e^{15}\right ) x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{\left (-729-e^{15}\right ) x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx\\ &=\int \frac {2 x \left (-e^{15} x^3-e^{10} x \left (-1-x+27 x^2+9 x^3\right )-e^5 \left (1-18 x-24 x^2+240 x^3+162 x^4+27 x^5\right )-3 \left (3-26 x-46 x^2+231 x^3+243 x^4+81 x^5+9 x^6\right )+\left (3 e^{15} x^2+e^{10} \left (-1-3 x+81 x^2+27 x^3\right )+e^5 \left (-17-60 x+717 x^2+486 x^3+81 x^4\right )+9 \left (-8-33 x+230 x^2+242 x^3+81 x^4+9 x^5\right )\right ) \log (x)-\left (3 e^{15} x+e^{10} \left (-2+81 x+27 x^2\right )+9 e^5 \left (-4+80 x+54 x^2+9 x^3\right )+9 \left (-18+234 x+242 x^2+81 x^3+9 x^4\right )\right ) \log ^2(x)+\left (9+e^5+3 x\right )^3 \log ^3(x)\right )}{\left (9+e^5+3 x\right )^3 (x-\log (x))^3} \, dx\\ &=2 \int \frac {x \left (-e^{15} x^3-e^{10} x \left (-1-x+27 x^2+9 x^3\right )-e^5 \left (1-18 x-24 x^2+240 x^3+162 x^4+27 x^5\right )-3 \left (3-26 x-46 x^2+231 x^3+243 x^4+81 x^5+9 x^6\right )+\left (3 e^{15} x^2+e^{10} \left (-1-3 x+81 x^2+27 x^3\right )+e^5 \left (-17-60 x+717 x^2+486 x^3+81 x^4\right )+9 \left (-8-33 x+230 x^2+242 x^3+81 x^4+9 x^5\right )\right ) \log (x)-\left (3 e^{15} x+e^{10} \left (-2+81 x+27 x^2\right )+9 e^5 \left (-4+80 x+54 x^2+9 x^3\right )+9 \left (-18+234 x+242 x^2+81 x^3+9 x^4\right )\right ) \log ^2(x)+\left (9+e^5+3 x\right )^3 \log ^3(x)\right )}{\left (9+e^5+3 x\right )^3 (x-\log (x))^3} \, dx\\ &=2 \int \left (-x+\frac {(-1+x) x}{\left (9+e^5+3 x\right )^2 (x-\log (x))^3}+\frac {x \left (72+17 e^5+e^{10}-\left (27+12 e^5+e^{10}\right ) x-3 \left (15+2 e^5\right ) x^2-9 x^3\right )}{\left (9+e^5+3 x\right )^3 (x-\log (x))^2}+\frac {x \left (18+2 e^5+3 x\right )}{\left (9+e^5+3 x\right )^2 (x-\log (x))}\right ) \, dx\\ &=-x^2+2 \int \frac {(-1+x) x}{\left (9+e^5+3 x\right )^2 (x-\log (x))^3} \, dx+2 \int \frac {x \left (72+17 e^5+e^{10}-\left (27+12 e^5+e^{10}\right ) x-3 \left (15+2 e^5\right ) x^2-9 x^3\right )}{\left (9+e^5+3 x\right )^3 (x-\log (x))^2} \, dx+2 \int \frac {x \left (18+2 e^5+3 x\right )}{\left (9+e^5+3 x\right )^2 (x-\log (x))} \, dx\\ &=-x^2+2 \int \left (\frac {1}{9 (x-\log (x))^3}+\frac {108+21 e^5+e^{10}}{9 \left (9+e^5+3 x\right )^2 (x-\log (x))^3}+\frac {-21-2 e^5}{9 \left (9+e^5+3 x\right ) (x-\log (x))^3}\right ) \, dx+2 \int \left (\frac {12+e^5}{9 (x-\log (x))^2}-\frac {x}{3 (x-\log (x))^2}+\frac {\left (9+e^5\right )^2}{3 \left (9+e^5+3 x\right )^3 (x-\log (x))^2}+\frac {-9-e^5}{3 \left (9+e^5+3 x\right )^2 (x-\log (x))^2}+\frac {-108-21 e^5-e^{10}}{9 \left (9+e^5+3 x\right ) (x-\log (x))^2}\right ) \, dx+2 \int \left (\frac {1}{3 (x-\log (x))}-\frac {\left (9+e^5\right )^2}{3 \left (9+e^5+3 x\right )^2 (x-\log (x))}\right ) \, dx\\ &=-x^2+\frac {2}{9} \int \frac {1}{(x-\log (x))^3} \, dx-\frac {2}{3} \int \frac {x}{(x-\log (x))^2} \, dx+\frac {2}{3} \int \frac {1}{x-\log (x)} \, dx-\frac {1}{3} \left (2 \left (9+e^5\right )\right ) \int \frac {1}{\left (9+e^5+3 x\right )^2 (x-\log (x))^2} \, dx+\frac {1}{3} \left (2 \left (9+e^5\right )^2\right ) \int \frac {1}{\left (9+e^5+3 x\right )^3 (x-\log (x))^2} \, dx-\frac {1}{3} \left (2 \left (9+e^5\right )^2\right ) \int \frac {1}{\left (9+e^5+3 x\right )^2 (x-\log (x))} \, dx+\frac {1}{9} \left (2 \left (12+e^5\right )\right ) \int \frac {1}{(x-\log (x))^2} \, dx-\frac {1}{9} \left (2 \left (21+2 e^5\right )\right ) \int \frac {1}{\left (9+e^5+3 x\right ) (x-\log (x))^3} \, dx+\frac {1}{9} \left (2 \left (108+21 e^5+e^{10}\right )\right ) \int \frac {1}{\left (9+e^5+3 x\right )^2 (x-\log (x))^3} \, dx-\frac {1}{9} \left (2 \left (108+21 e^5+e^{10}\right )\right ) \int \frac {1}{\left (9+e^5+3 x\right ) (x-\log (x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.24, size = 46, normalized size = 1.64 \begin {gather*} -x^2 \left (1+\frac {1}{\left (9+e^5+3 x\right )^2 (x-\log (x))^2}+\frac {2}{\left (9+e^5+3 x\right ) (-x+\log (x))}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(18*x - 156*x^2 - 276*x^3 + 1386*x^4 + 2*E^15*x^4 + 1458*x^5 + 486*x^6 + 54*x^7 + E^10*(-2*x^2 - 2*x
^3 + 54*x^4 + 18*x^5) + E^5*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) + (144*x + 594*x^2 - 4140*x^3
- 6*E^15*x^3 - 4356*x^4 - 1458*x^5 - 162*x^6 + E^10*(2*x + 6*x^2 - 162*x^3 - 54*x^4) + E^5*(34*x + 120*x^2 -
1434*x^3 - 972*x^4 - 162*x^5))*Log[x] + (-324*x + 4212*x^2 + 6*E^15*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5 + E^10
*(-4*x + 162*x^2 + 54*x^3) + E^5*(-72*x + 1440*x^2 + 972*x^3 + 162*x^4))*Log[x]^2 + (-1458*x - 2*E^15*x - 1458
*x^2 - 486*x^3 - 54*x^4 + E^10*(-54*x - 18*x^2) + E^5*(-486*x - 324*x^2 - 54*x^3))*Log[x]^3)/(-729*x^3 - E^15*
x^3 - 729*x^4 - 243*x^5 - 27*x^6 + E^10*(-27*x^3 - 9*x^4) + E^5*(-243*x^3 - 162*x^4 - 27*x^5) + (2187*x^2 + 3*
E^15*x^2 + 2187*x^3 + 729*x^4 + 81*x^5 + E^10*(81*x^2 + 27*x^3) + E^5*(729*x^2 + 486*x^3 + 81*x^4))*Log[x] + (
-2187*x - 3*E^15*x - 2187*x^2 - 729*x^3 - 81*x^4 + E^10*(-81*x - 27*x^2) + E^5*(-729*x - 486*x^2 - 81*x^3))*Lo
g[x]^2 + (729 + E^15 + 729*x + 243*x^2 + 27*x^3 + E^10*(27 + 9*x) + E^5*(243 + 162*x + 27*x^2))*Log[x]^3),x]

[Out]

-(x^2*(1 + 1/((9 + E^5 + 3*x)^2*(x - Log[x])^2) + 2/((9 + E^5 + 3*x)*(-x + Log[x]))))

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fricas [B]  time = 0.72, size = 236, normalized size = 8.43 \begin {gather*} -\frac {9 \, x^{6} + 54 \, x^{5} + x^{4} e^{10} + 75 \, x^{4} - 18 \, x^{3} + {\left (9 \, x^{4} + 54 \, x^{3} + x^{2} e^{10} + 81 \, x^{2} + 6 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \relax (x)^{2} + x^{2} + 2 \, {\left (3 \, x^{5} + 9 \, x^{4} - x^{3}\right )} e^{5} - 2 \, {\left (9 \, x^{5} + 54 \, x^{4} + x^{3} e^{10} + 78 \, x^{3} - 9 \, x^{2} + {\left (6 \, x^{4} + 18 \, x^{3} - x^{2}\right )} e^{5}\right )} \log \relax (x)}{9 \, x^{4} + 54 \, x^{3} + x^{2} e^{10} + {\left (9 \, x^{2} + 6 \, {\left (x + 3\right )} e^{5} + 54 \, x + e^{10} + 81\right )} \log \relax (x)^{2} + 81 \, x^{2} + 6 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5} - 2 \, {\left (9 \, x^{3} + 54 \, x^{2} + x e^{10} + 6 \, {\left (x^{2} + 3 \, x\right )} e^{5} + 81 \, x\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5)-54*x^4-486*x^3-1458*x^2-1458*
x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*
x^4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x)*exp(5)^2+(-162*x^5-972*x^4-
1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+
54*x^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^7+486*x^6+1458*x^5+1386*x^
4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x
)^3+(-3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x^3-2187*x^2-2187*x)*log(
x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2
)*log(x)-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-243*x^5-729*x^4-729*x^3
),x, algorithm="fricas")

[Out]

-(9*x^6 + 54*x^5 + x^4*e^10 + 75*x^4 - 18*x^3 + (9*x^4 + 54*x^3 + x^2*e^10 + 81*x^2 + 6*(x^3 + 3*x^2)*e^5)*log
(x)^2 + x^2 + 2*(3*x^5 + 9*x^4 - x^3)*e^5 - 2*(9*x^5 + 54*x^4 + x^3*e^10 + 78*x^3 - 9*x^2 + (6*x^4 + 18*x^3 -
x^2)*e^5)*log(x))/(9*x^4 + 54*x^3 + x^2*e^10 + (9*x^2 + 6*(x + 3)*e^5 + 54*x + e^10 + 81)*log(x)^2 + 81*x^2 +
6*(x^3 + 3*x^2)*e^5 - 2*(9*x^3 + 54*x^2 + x*e^10 + 6*(x^2 + 3*x)*e^5 + 81*x)*log(x))

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giac [B]  time = 0.47, size = 302, normalized size = 10.79 \begin {gather*} -\frac {9 \, x^{6} + 6 \, x^{5} e^{5} - 18 \, x^{5} \log \relax (x) - 12 \, x^{4} e^{5} \log \relax (x) + 9 \, x^{4} \log \relax (x)^{2} + 6 \, x^{3} e^{5} \log \relax (x)^{2} + 54 \, x^{5} + x^{4} e^{10} + 18 \, x^{4} e^{5} - 108 \, x^{4} \log \relax (x) - 2 \, x^{3} e^{10} \log \relax (x) - 36 \, x^{3} e^{5} \log \relax (x) + 54 \, x^{3} \log \relax (x)^{2} + x^{2} e^{10} \log \relax (x)^{2} + 18 \, x^{2} e^{5} \log \relax (x)^{2} + 75 \, x^{4} - 2 \, x^{3} e^{5} - 156 \, x^{3} \log \relax (x) + 2 \, x^{2} e^{5} \log \relax (x) + 81 \, x^{2} \log \relax (x)^{2} - 18 \, x^{3} + 18 \, x^{2} \log \relax (x) + x^{2}}{9 \, x^{4} + 6 \, x^{3} e^{5} - 18 \, x^{3} \log \relax (x) - 12 \, x^{2} e^{5} \log \relax (x) + 9 \, x^{2} \log \relax (x)^{2} + 6 \, x e^{5} \log \relax (x)^{2} + 54 \, x^{3} + x^{2} e^{10} + 18 \, x^{2} e^{5} - 108 \, x^{2} \log \relax (x) - 2 \, x e^{10} \log \relax (x) - 36 \, x e^{5} \log \relax (x) + 54 \, x \log \relax (x)^{2} + e^{10} \log \relax (x)^{2} + 18 \, e^{5} \log \relax (x)^{2} + 81 \, x^{2} - 162 \, x \log \relax (x) + 81 \, \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5)-54*x^4-486*x^3-1458*x^2-1458*
x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*
x^4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x)*exp(5)^2+(-162*x^5-972*x^4-
1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+
54*x^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^7+486*x^6+1458*x^5+1386*x^
4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x
)^3+(-3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x^3-2187*x^2-2187*x)*log(
x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2
)*log(x)-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-243*x^5-729*x^4-729*x^3
),x, algorithm="giac")

[Out]

-(9*x^6 + 6*x^5*e^5 - 18*x^5*log(x) - 12*x^4*e^5*log(x) + 9*x^4*log(x)^2 + 6*x^3*e^5*log(x)^2 + 54*x^5 + x^4*e
^10 + 18*x^4*e^5 - 108*x^4*log(x) - 2*x^3*e^10*log(x) - 36*x^3*e^5*log(x) + 54*x^3*log(x)^2 + x^2*e^10*log(x)^
2 + 18*x^2*e^5*log(x)^2 + 75*x^4 - 2*x^3*e^5 - 156*x^3*log(x) + 2*x^2*e^5*log(x) + 81*x^2*log(x)^2 - 18*x^3 +
18*x^2*log(x) + x^2)/(9*x^4 + 6*x^3*e^5 - 18*x^3*log(x) - 12*x^2*e^5*log(x) + 9*x^2*log(x)^2 + 6*x*e^5*log(x)^
2 + 54*x^3 + x^2*e^10 + 18*x^2*e^5 - 108*x^2*log(x) - 2*x*e^10*log(x) - 36*x*e^5*log(x) + 54*x*log(x)^2 + e^10
*log(x)^2 + 18*e^5*log(x)^2 + 81*x^2 - 162*x*log(x) + 81*log(x)^2)

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maple [B]  time = 0.08, size = 58, normalized size = 2.07

method	result	size
risch	\(-x^{2}+\frac {\left (2 x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{5} \ln \relax (x )+6 x^{2}-6 x \ln \relax (x )+18 x -18 \ln \relax (x )-1\right ) x^{2}}{\left (9+{\mathrm e}^{5}+3 x \right )^{2} \left (x -\ln \relax (x )\right )^{2}}\)	\(58\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5)-54*x^4-486*x^3-1458*x^2-1458*x)*ln(
x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^4+435
6*x^3+4212*x^2-324*x)*ln(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x)*exp(5)^2+(-162*x^5-972*x^4-1434*x^3
+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*ln(x)+2*x^4*exp(5)^3+(18*x^5+54*x^4-2*
x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^7+486*x^6+1458*x^5+1386*x^4-276*x^3
-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*ln(x)^3+(-3*x*
exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x^3-2187*x^2-2187*x)*ln(x)^2+(3*x^2
*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*ln(x)-x^3
*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-243*x^5-729*x^4-729*x^3),x,method=_
RETURNVERBOSE)

[Out]

-x^2+(2*x*exp(5)-2*exp(5)*ln(x)+6*x^2-6*x*ln(x)+18*x-18*ln(x)-1)*x^2/(9+exp(5)+3*x)^2/(x-ln(x))^2

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maxima [B]  time = 0.51, size = 196, normalized size = 7.00 \begin {gather*} -\frac {9 \, x^{6} + 6 \, x^{5} {\left (e^{5} + 9\right )} + x^{4} {\left (e^{10} + 18 \, e^{5} + 75\right )} - 2 \, x^{3} {\left (e^{5} + 9\right )} + {\left (9 \, x^{4} + 6 \, x^{3} {\left (e^{5} + 9\right )} + x^{2} {\left (e^{10} + 18 \, e^{5} + 81\right )}\right )} \log \relax (x)^{2} + x^{2} - 2 \, {\left (9 \, x^{5} + 6 \, x^{4} {\left (e^{5} + 9\right )} + x^{3} {\left (e^{10} + 18 \, e^{5} + 78\right )} - x^{2} {\left (e^{5} + 9\right )}\right )} \log \relax (x)}{9 \, x^{4} + 6 \, x^{3} {\left (e^{5} + 9\right )} + x^{2} {\left (e^{10} + 18 \, e^{5} + 81\right )} + {\left (9 \, x^{2} + 6 \, x {\left (e^{5} + 9\right )} + e^{10} + 18 \, e^{5} + 81\right )} \log \relax (x)^{2} - 2 \, {\left (9 \, x^{3} + 6 \, x^{2} {\left (e^{5} + 9\right )} + x {\left (e^{10} + 18 \, e^{5} + 81\right )}\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5)-54*x^4-486*x^3-1458*x^2-1458*
x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*
x^4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x)*exp(5)^2+(-162*x^5-972*x^4-
1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+
54*x^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^7+486*x^6+1458*x^5+1386*x^
4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x
)^3+(-3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x^3-2187*x^2-2187*x)*log(
x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2
)*log(x)-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-243*x^5-729*x^4-729*x^3
),x, algorithm="maxima")

[Out]

-(9*x^6 + 6*x^5*(e^5 + 9) + x^4*(e^10 + 18*e^5 + 75) - 2*x^3*(e^5 + 9) + (9*x^4 + 6*x^3*(e^5 + 9) + x^2*(e^10
+ 18*e^5 + 81))*log(x)^2 + x^2 - 2*(9*x^5 + 6*x^4*(e^5 + 9) + x^3*(e^10 + 18*e^5 + 78) - x^2*(e^5 + 9))*log(x)
)/(9*x^4 + 6*x^3*(e^5 + 9) + x^2*(e^10 + 18*e^5 + 81) + (9*x^2 + 6*x*(e^5 + 9) + e^10 + 18*e^5 + 81)*log(x)^2
- 2*(9*x^3 + 6*x^2*(e^5 + 9) + x*(e^10 + 18*e^5 + 81))*log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {18\,x+{\mathrm {e}}^5\,\left (54\,x^6+324\,x^5+480\,x^4-48\,x^3-36\,x^2+2\,x\right )-{\ln \relax (x)}^3\,\left (1458\,x+{\mathrm {e}}^{10}\,\left (18\,x^2+54\,x\right )+2\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (54\,x^3+324\,x^2+486\,x\right )+1458\,x^2+486\,x^3+54\,x^4\right )+{\ln \relax (x)}^2\,\left ({\mathrm {e}}^{10}\,\left (54\,x^3+162\,x^2-4\,x\right )-324\,x+6\,x^2\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (162\,x^4+972\,x^3+1440\,x^2-72\,x\right )+4212\,x^2+4356\,x^3+1458\,x^4+162\,x^5\right )+2\,x^4\,{\mathrm {e}}^{15}-\ln \relax (x)\,\left (6\,x^3\,{\mathrm {e}}^{15}-144\,x-{\mathrm {e}}^{10}\,\left (-54\,x^4-162\,x^3+6\,x^2+2\,x\right )+{\mathrm {e}}^5\,\left (162\,x^5+972\,x^4+1434\,x^3-120\,x^2-34\,x\right )-594\,x^2+4140\,x^3+4356\,x^4+1458\,x^5+162\,x^6\right )-156\,x^2-276\,x^3+1386\,x^4+1458\,x^5+486\,x^6+54\,x^7-{\mathrm {e}}^{10}\,\left (-18\,x^5-54\,x^4+2\,x^3+2\,x^2\right )}{{\ln \relax (x)}^2\,\left (2187\,x+{\mathrm {e}}^{10}\,\left (27\,x^2+81\,x\right )+3\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (81\,x^3+486\,x^2+729\,x\right )+2187\,x^2+729\,x^3+81\,x^4\right )-\ln \relax (x)\,\left ({\mathrm {e}}^{10}\,\left (27\,x^3+81\,x^2\right )+3\,x^2\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (81\,x^4+486\,x^3+729\,x^2\right )+2187\,x^2+2187\,x^3+729\,x^4+81\,x^5\right )+{\mathrm {e}}^{10}\,\left (9\,x^4+27\,x^3\right )+x^3\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (27\,x^5+162\,x^4+243\,x^3\right )+729\,x^3+729\,x^4+243\,x^5+27\,x^6-{\ln \relax (x)}^3\,\left (729\,x+{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (27\,x^2+162\,x+243\right )+243\,x^2+27\,x^3+{\mathrm {e}}^{10}\,\left (9\,x+27\right )+729\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(18*x + exp(5)*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) - log(x)^3*(1458*x + exp(10)*(54*x +
18*x^2) + 2*x*exp(15) + exp(5)*(486*x + 324*x^2 + 54*x^3) + 1458*x^2 + 486*x^3 + 54*x^4) + log(x)^2*(exp(10)*(
162*x^2 - 4*x + 54*x^3) - 324*x + 6*x^2*exp(15) + exp(5)*(1440*x^2 - 72*x + 972*x^3 + 162*x^4) + 4212*x^2 + 43
56*x^3 + 1458*x^4 + 162*x^5) + 2*x^4*exp(15) - log(x)*(6*x^3*exp(15) - 144*x - exp(10)*(2*x + 6*x^2 - 162*x^3
- 54*x^4) + exp(5)*(1434*x^3 - 120*x^2 - 34*x + 972*x^4 + 162*x^5) - 594*x^2 + 4140*x^3 + 4356*x^4 + 1458*x^5
+ 162*x^6) - 156*x^2 - 276*x^3 + 1386*x^4 + 1458*x^5 + 486*x^6 + 54*x^7 - exp(10)*(2*x^2 + 2*x^3 - 54*x^4 - 18
*x^5))/(log(x)^2*(2187*x + exp(10)*(81*x + 27*x^2) + 3*x*exp(15) + exp(5)*(729*x + 486*x^2 + 81*x^3) + 2187*x^
2 + 729*x^3 + 81*x^4) - log(x)*(exp(10)*(81*x^2 + 27*x^3) + 3*x^2*exp(15) + exp(5)*(729*x^2 + 486*x^3 + 81*x^4
) + 2187*x^2 + 2187*x^3 + 729*x^4 + 81*x^5) + exp(10)*(27*x^3 + 9*x^4) + x^3*exp(15) + exp(5)*(243*x^3 + 162*x
^4 + 27*x^5) + 729*x^3 + 729*x^4 + 243*x^5 + 27*x^6 - log(x)^3*(729*x + exp(15) + exp(5)*(162*x + 27*x^2 + 243
) + 243*x^2 + 27*x^3 + exp(10)*(9*x + 27) + 729)),x)

[Out]

int(-(18*x + exp(5)*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) - log(x)^3*(1458*x + exp(10)*(54*x +
18*x^2) + 2*x*exp(15) + exp(5)*(486*x + 324*x^2 + 54*x^3) + 1458*x^2 + 486*x^3 + 54*x^4) + log(x)^2*(exp(10)*(
162*x^2 - 4*x + 54*x^3) - 324*x + 6*x^2*exp(15) + exp(5)*(1440*x^2 - 72*x + 972*x^3 + 162*x^4) + 4212*x^2 + 43
56*x^3 + 1458*x^4 + 162*x^5) + 2*x^4*exp(15) - log(x)*(6*x^3*exp(15) - 144*x - exp(10)*(2*x + 6*x^2 - 162*x^3
- 54*x^4) + exp(5)*(1434*x^3 - 120*x^2 - 34*x + 972*x^4 + 162*x^5) - 594*x^2 + 4140*x^3 + 4356*x^4 + 1458*x^5
+ 162*x^6) - 156*x^2 - 276*x^3 + 1386*x^4 + 1458*x^5 + 486*x^6 + 54*x^7 - exp(10)*(2*x^2 + 2*x^3 - 54*x^4 - 18
*x^5))/(log(x)^2*(2187*x + exp(10)*(81*x + 27*x^2) + 3*x*exp(15) + exp(5)*(729*x + 486*x^2 + 81*x^3) + 2187*x^
2 + 729*x^3 + 81*x^4) - log(x)*(exp(10)*(81*x^2 + 27*x^3) + 3*x^2*exp(15) + exp(5)*(729*x^2 + 486*x^3 + 81*x^4
) + 2187*x^2 + 2187*x^3 + 729*x^4 + 81*x^5) + exp(10)*(27*x^3 + 9*x^4) + x^3*exp(15) + exp(5)*(243*x^3 + 162*x
^4 + 27*x^5) + 729*x^3 + 729*x^4 + 243*x^5 + 27*x^6 - log(x)^3*(729*x + exp(15) + exp(5)*(162*x + 27*x^2 + 243
) + 243*x^2 + 27*x^3 + exp(10)*(9*x + 27) + 729)), x)

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sympy [B]  time = 0.62, size = 158, normalized size = 5.64 \begin {gather*} - x^{2} + \frac {6 x^{4} + 18 x^{3} + 2 x^{3} e^{5} - x^{2} + \left (- 6 x^{3} - 2 x^{2} e^{5} - 18 x^{2}\right ) \log {\relax (x )}}{9 x^{4} + 54 x^{3} + 6 x^{3} e^{5} + 81 x^{2} + 18 x^{2} e^{5} + x^{2} e^{10} + \left (9 x^{2} + 54 x + 6 x e^{5} + 81 + 18 e^{5} + e^{10}\right ) \log {\relax (x )}^{2} + \left (- 18 x^{3} - 12 x^{2} e^{5} - 108 x^{2} - 2 x e^{10} - 36 x e^{5} - 162 x\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(5)**3+(-18*x**2-54*x)*exp(5)**2+(-54*x**3-324*x**2-486*x)*exp(5)-54*x**4-486*x**3-1458*x*
*2-1458*x)*ln(x)**3+(6*x**2*exp(5)**3+(54*x**3+162*x**2-4*x)*exp(5)**2+(162*x**4+972*x**3+1440*x**2-72*x)*exp(
5)+162*x**5+1458*x**4+4356*x**3+4212*x**2-324*x)*ln(x)**2+(-6*x**3*exp(5)**3+(-54*x**4-162*x**3+6*x**2+2*x)*ex
p(5)**2+(-162*x**5-972*x**4-1434*x**3+120*x**2+34*x)*exp(5)-162*x**6-1458*x**5-4356*x**4-4140*x**3+594*x**2+14
4*x)*ln(x)+2*x**4*exp(5)**3+(18*x**5+54*x**4-2*x**3-2*x**2)*exp(5)**2+(54*x**6+324*x**5+480*x**4-48*x**3-36*x*
*2+2*x)*exp(5)+54*x**7+486*x**6+1458*x**5+1386*x**4-276*x**3-156*x**2+18*x)/((exp(5)**3+(9*x+27)*exp(5)**2+(27
*x**2+162*x+243)*exp(5)+27*x**3+243*x**2+729*x+729)*ln(x)**3+(-3*x*exp(5)**3+(-27*x**2-81*x)*exp(5)**2+(-81*x*
*3-486*x**2-729*x)*exp(5)-81*x**4-729*x**3-2187*x**2-2187*x)*ln(x)**2+(3*x**2*exp(5)**3+(27*x**3+81*x**2)*exp(
5)**2+(81*x**4+486*x**3+729*x**2)*exp(5)+81*x**5+729*x**4+2187*x**3+2187*x**2)*ln(x)-x**3*exp(5)**3+(-9*x**4-2
7*x**3)*exp(5)**2+(-27*x**5-162*x**4-243*x**3)*exp(5)-27*x**6-243*x**5-729*x**4-729*x**3),x)

[Out]

-x**2 + (6*x**4 + 18*x**3 + 2*x**3*exp(5) - x**2 + (-6*x**3 - 2*x**2*exp(5) - 18*x**2)*log(x))/(9*x**4 + 54*x*
*3 + 6*x**3*exp(5) + 81*x**2 + 18*x**2*exp(5) + x**2*exp(10) + (9*x**2 + 54*x + 6*x*exp(5) + 81 + 18*exp(5) +
exp(10))*log(x)**2 + (-18*x**3 - 12*x**2*exp(5) - 108*x**2 - 2*x*exp(10) - 36*x*exp(5) - 162*x)*log(x))

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