∫ −192x6−96x7+e5(−192x3−240x4−72x5−48x6−24x7)+(−96x6+e5(−192x3−120x4−24x6)) log(3)−48e5x3 log2(3)+ex∕4(80x6+48x7+4x8+e5(64x3+84x4+28x5+21x6+12x7+x8)+(48x6+8x7+e5(64x3+44x4+2x5+12x6+2x7)) log(3)+(4x6+e5(16x3+x4+x6)) log2(3))_____________________________________________________________________________________________________________________________________________________________________________________________ 256x6+e15(4+12x2+12x4+4x6)+e10(48x2+96x4+48x6)+e5(192x4+192x6) dx

3.82.43 \(\int \frac {-192 x^6-96 x^7+e^5 (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7)+(-96 x^6+e^5 (-192 x^3-120 x^4-24 x^6)) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} (80 x^6+48 x^7+4 x^8+e^5 (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8)+(48 x^6+8 x^7+e^5 (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7)) \log (3)+(4 x^6+e^5 (16 x^3+x^4+x^6)) \log ^2(3))}{256 x^6+e^{15} (4+12 x^2+12 x^4+4 x^6)+e^{10} (48 x^2+96 x^4+48 x^6)+e^5 (192 x^4+192 x^6)} \, dx\)

Optimal. Leaf size=31 \[ \frac {\left (-3+e^{x/4}\right ) (2+x+\log (3))^2}{\left (4+e^5+\frac {e^5}{x^2}\right )^2} \]

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Rubi [F] time = 11.26, 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 {-192 x^6-96 x^7+e^5 \left (-192 x^3-240 x^4-72 x^5-48 x^6-24 x^7\right )+\left (-96 x^6+e^5 \left (-192 x^3-120 x^4-24 x^6\right )\right ) \log (3)-48 e^5 x^3 \log ^2(3)+e^{x/4} \left (80 x^6+48 x^7+4 x^8+e^5 \left (64 x^3+84 x^4+28 x^5+21 x^6+12 x^7+x^8\right )+\left (48 x^6+8 x^7+e^5 \left (64 x^3+44 x^4+2 x^5+12 x^6+2 x^7\right )\right ) \log (3)+\left (4 x^6+e^5 \left (16 x^3+x^4+x^6\right )\right ) \log ^2(3)\right )}{256 x^6+e^{15} \left (4+12 x^2+12 x^4+4 x^6\right )+e^{10} \left (48 x^2+96 x^4+48 x^6\right )+e^5 \left (192 x^4+192 x^6\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-192*x^6 - 96*x^7 + E^5*(-192*x^3 - 240*x^4 - 72*x^5 - 48*x^6 - 24*x^7) + (-96*x^6 + E^5*(-192*x^3 - 120*

x^4 - 24*x^6))*Log[3] - 48*E^5*x^3*Log[3]^2 + E^(x/4)*(80*x^6 + 48*x^7 + 4*x^8 + E^5*(64*x^3 + 84*x^4 + 28*x^5

+ 21*x^6 + 12*x^7 + x^8) + (48*x^6 + 8*x^7 + E^5*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7))*Log[3] + (4*x^6

+ E^5*(16*x^3 + x^4 + x^6))*Log[3]^2))/(256*x^6 + E^15*(4 + 12*x^2 + 12*x^4 + 4*x^6) + E^10*(48*x^2 + 96*x^4 +

48*x^6) + E^5*(192*x^4 + 192*x^6)),x]

[Out]

(32*E^(x/4))/(4 + E^5)^2 - (8*E^(x/4)*x)/(4 + E^5)^2 + (E^(x/4)*x^2)/(4 + E^5)^2 - (3*x^4*(2 + x + Log[3])^2)/

(E^5 + (4 + E^5)*x^2)^2 - (4*E^(x/4)*(12 + Log[9]))/(4 + E^5)^2 + (E^(x/4)*x*(12 + Log[9]))/(4 + E^5)^2 - (E^(

5/2 - ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(2*E^(5/2)

*Sqrt[4 + E^5]*(4 + Log[9]) - I*(96 + 4*Log[3]^2 + E^5*(27 + 8*Log[3] - 2*Log[3]^2) + Log[3]*(32 - 3*Log[81]))

))/(8*(4 + E^5)^(7/2)) - (E^(5/2 + ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[-1/4*(I*E^(5/2) - Sqrt[4 + E^5

]*x)/Sqrt[4 + E^5]]*(2*E^(5/2)*Sqrt[4 + E^5]*(4 + Log[9]) + I*(96 + 4*Log[3]^2 + E^5*(27 + 8*Log[3] - 2*Log[3]

^2) + Log[3]*(32 - 3*Log[81]))))/(8*(4 + E^5)^(7/2)) - ((I/64)*E^(15/2 + x/4)*(256 + 4*Log[3]^2 + 32*E^5*(2 +

Log[3]) + Log[3]*(128 - Log[81])))/((4 + E^5)^(7/2)*(I*E^(5/2) - Sqrt[4 + E^5]*x)^2) + ((I/256)*E^(15/2 + x/4)

*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/((4 + E^5)^4*(I*E^(5/2) - Sqrt[4 + E^5]*x)

) + ((I/64)*E^(15/2 + x/4)*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/((4 + E^5)^(7/2)

*(I*E^(5/2) + Sqrt[4 + E^5]*x)^2) + (3*E^(5 + x/4)*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log

[81])))/(64*(4 + E^5)^(7/2)*(I*E^(5/2) + Sqrt[4 + E^5]*x)) - (3*E^(5 + x/4)*(256 + 4*Log[3]^2 + 32*E^5*(2 + Lo

g[3]) + Log[3]*(128 - Log[81])))/(64*(4 + E^5)^3*(I*E^(5/2)*Sqrt[4 + E^5] - (4 + E^5)*x)) + ((I/256)*E^(15/2 +

x/4)*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/((4 + E^5)^(3/2)*(I*(E*(4 + E^5))^(5/

2) + (4 + E^5)^3*x)) + ((I/1024)*E^(15/2 + ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[-1/4*(I*E^(5/2) - Sqrt

[4 + E^5]*x)/Sqrt[4 + E^5]]*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/(4 + E^5)^(9/2)

- (((3*I)/64)*E^(5/2 + ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[-1/4*(I*E^(5/2) - Sqrt[4 + E^5]*x)/Sqrt[4

+ E^5]]*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/(4 + E^5)^(7/2) - ((I/1024)*E^(15/

2 - ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(256 + 4*Log

[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/(4 + E^5)^(9/2) - (3*E^(5 - ((I/4)*E^(5/2))/Sqrt[4 + E^

5])*ExpIntegralEi[(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + L

og[3]*(128 - Log[81])))/(256*(4 + E^5)^4) + (((3*I)/64)*E^(5/2 - ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[

(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[8

1])))/(4 + E^5)^(7/2) - (3*E^(5 + ((I/4)*E^(5/2))/Sqrt[4 + E^5])*ExpIntegralEi[-1/4*(I*E^(5/2)*Sqrt[4 + E^5] -

(4 + E^5)*x)/(4 + E^5)]*(256 + 4*Log[3]^2 + 32*E^5*(2 + Log[3]) + Log[3]*(128 - Log[81])))/(256*(4 + E^5)^4)

- (E^(5 + x/4)*(432 + 208*Log[3] + 8*Log[3]^2 + E^5*(109 + 52*Log[3] - Log[3]^2) - Log[27]*Log[81]))/(16*(4 +

E^5)^(7/2)*(I*E^(5/2) + Sqrt[4 + E^5]*x)) + (E^(5 + x/4)*(432 + 208*Log[3] + 8*Log[3]^2 + E^5*(109 + 52*Log[3]

- Log[3]^2) - Log[27]*Log[81]))/(16*(4 + E^5)^3*(I*E^(5/2)*Sqrt[4 + E^5] - (4 + E^5)*x)) + (E^(5 - ((I/4)*E^(

5/2))/Sqrt[4 + E^5])*ExpIntegralEi[(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(432 + 208*Log[3] + 8*Log[

3]^2 + E^5*(109 + 52*Log[3] - Log[3]^2) - Log[27]*Log[81]))/(64*(4 + E^5)^4) - ((I/16)*E^(5/2 - ((I/4)*E^(5/2)

)/Sqrt[4 + E^5])*ExpIntegralEi[(I*E^(5/2) + Sqrt[4 + E^5]*x)/(4*Sqrt[4 + E^5])]*(432 + 208*Log[3] + 8*Log[3]^2

+ E^5*(109 + 52*Log[3] - Log[3]^2) - Log[27]*Log[81]))/(4 + E^5)^(7/2) + (E^(5 + ((I/4)*E^(5/2))/Sqrt[4 + E^5

])*ExpIntegralEi[-1/4*(I*E^(5/2)*Sqrt[4 + E^5] - (4 + E^5)*x)/(4 + E^5)]*(432 + 208*Log[3] + 8*Log[3]^2 + E^5*

(109 + 52*Log[3] - Log[3]^2) - Log[27]*Log[81]))/(64*(4 + E^5)^4) + ((I/16)*E^(5/2 + ((I/4)*E^(5/2))/Sqrt[4 +

E^5])*ExpIntegralEi[-1/4*(I*E^(5/2)*Sqrt[4 + E^5] - (4 + E^5)*x)/(4 + E^5)]*(432 + 208*Log[3] + 8*Log[3]^2 + E

^5*(109 + 52*Log[3] - Log[3]^2) - Log[27]*Log[81]))/(4 + E^5)^(7/2) + (E^(x/4)*(80 + E^5*(18 + 12*Log[3] + Log

[3]^2) + Log[3]*(48 + Log[81])))/(4 + E^5)^3 - (4*(16*(2 + Log[3])^2 + 4*E^5*(7 + 8*Log[3] + 2*Log[3]^2) + E^1

0*(3 + Log[3]^2 + Log[81]))*Defer[Int][(E^(10 + x/4)*x)/(E^5 + (4 + E^5)*x^2)^3, x])/(4 + E^5)^3 + ((64*(2 + L

og[3])^2 + E^5*(44 + 64*Log[3] + 16*Log[3]^2 + Log[9]))*Defer[Int][(E^(5 + x/4)*x)/(E^5 + (4 + E^5)*x^2)^2, x]

)/(4*(4 + E^5)^2)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^3 (2+x+\log (3)) \left (-96 x^3+4 e^{x/4} x^3 (10+x+\log (3))+e^{5+\frac {x}{4}} \left (x^2+x^4+16 (2+\log (3))+x^3 (10+\log (3))+x (26+\log (3))\right )-24 e^5 \left (4+3 x+x^3+\log (9)\right )\right )}{4 \left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx\\ &=\frac {1}{4} \int \frac {x^3 (2+x+\log (3)) \left (-96 x^3+4 e^{x/4} x^3 (10+x+\log (3))+e^{5+\frac {x}{4}} \left (x^2+x^4+16 (2+\log (3))+x^3 (10+\log (3))+x (26+\log (3))\right )-24 e^5 \left (4+3 x+x^3+\log (9)\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx\\ &=\frac {1}{4} \int \left (\frac {24 x^3 (2+x+\log (3)) \left (-3 e^5 x-\left (4+e^5\right ) x^3-e^5 (4+\log (9))\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3}+\frac {e^{x/4} x^3 \left (4 \left (1+\frac {e^5}{4}\right ) x^5+28 e^5 x^2 \left (1+\frac {\log (3)}{14}\right )+64 e^5 \left (1+\frac {1}{4} \log (3) (4+\log (3))\right )+84 e^5 x \left (1+\frac {1}{84} \log (3) (44+\log (3))\right )+48 x^4 \left (1+\frac {1}{48} \left (4 \log (9)+e^5 (12+\log (9))\right )\right )+80 x^3 \left (1+\frac {1}{80} \left (e^5 \left (21+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right )\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3}\right ) \, dx\\ &=\frac {1}{4} \int \frac {e^{x/4} x^3 \left (4 \left (1+\frac {e^5}{4}\right ) x^5+28 e^5 x^2 \left (1+\frac {\log (3)}{14}\right )+64 e^5 \left (1+\frac {1}{4} \log (3) (4+\log (3))\right )+84 e^5 x \left (1+\frac {1}{84} \log (3) (44+\log (3))\right )+48 x^4 \left (1+\frac {1}{48} \left (4 \log (9)+e^5 (12+\log (9))\right )\right )+80 x^3 \left (1+\frac {1}{80} \left (e^5 \left (21+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right )\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx+6 \int \frac {x^3 (2+x+\log (3)) \left (-3 e^5 x-\left (4+e^5\right ) x^3-e^5 (4+\log (9))\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx\\ &=-\frac {3 x^4 (2+x+\log (3))^2}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {1}{4} \int \frac {e^{x/4} x^3 \left (e^5 \left (x^5+16 (2+\log (3))^2+x^3 \left (21+12 \log (3)+\log ^2(3)\right )+x \left (84+44 \log (3)+\log ^2(3)\right )+x^4 (12+\log (9))+x^2 (28+\log (9))\right )+x^3 \left (80+4 x^2+4 x (12+\log (9))+\log (3) (48+\log (81))\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx\\ &=-\frac {3 x^4 (2+x+\log (3))^2}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {1}{4} \int \left (\frac {e^{x/4} x^2}{\left (4+e^5\right )^2}+\frac {e^{x/4} x (12+\log (9))}{\left (4+e^5\right )^2}+\frac {e^{5+\frac {x}{4}} \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )-2 \left (4+e^5\right ) x (4+\log (9))+\log (3) (32-3 \log (81))\right )}{\left (4+e^5\right )^3 \left (e^5+\left (4+e^5\right ) x^2\right )}+\frac {e^{x/4} \left (80+e^5 \left (18+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right )}{\left (4+e^5\right )^3}+\frac {e^{5+\frac {x}{4}} \left (\left (4+e^5\right ) x \left (64 (2+\log (3))^2+e^5 \left (44+64 \log (3)+16 \log ^2(3)+\log (9)\right )\right )-e^5 \left (432+208 \log (3)+8 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )-\log (27) \log (81)\right )\right )}{\left (4+e^5\right )^3 \left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {e^{10+\frac {x}{4}} \left (e^5 \left (256+4 \log ^2(3)+32 e^5 (2+\log (3))+\log (3) (128-\log (81))\right )-16 x \left (16 (2+\log (3))^2+4 e^5 \left (7+8 \log (3)+2 \log ^2(3)\right )+e^{10} \left (3+\log ^2(3)+\log (81)\right )\right )\right )}{\left (4+e^5\right )^3 \left (e^5+\left (4+e^5\right ) x^2\right )^3}\right ) \, dx\\ &=-\frac {3 x^4 (2+x+\log (3))^2}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {\int \frac {e^{5+\frac {x}{4}} \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )-2 \left (4+e^5\right ) x (4+\log (9))+\log (3) (32-3 \log (81))\right )}{e^5+\left (4+e^5\right ) x^2} \, dx}{4 \left (4+e^5\right )^3}+\frac {\int \frac {e^{5+\frac {x}{4}} \left (\left (4+e^5\right ) x \left (64 (2+\log (3))^2+e^5 \left (44+64 \log (3)+16 \log ^2(3)+\log (9)\right )\right )-e^5 \left (432+208 \log (3)+8 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )-\log (27) \log (81)\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^2} \, dx}{4 \left (4+e^5\right )^3}+\frac {\int \frac {e^{10+\frac {x}{4}} \left (e^5 \left (256+4 \log ^2(3)+32 e^5 (2+\log (3))+\log (3) (128-\log (81))\right )-16 x \left (16 (2+\log (3))^2+4 e^5 \left (7+8 \log (3)+2 \log ^2(3)\right )+e^{10} \left (3+\log ^2(3)+\log (81)\right )\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx}{4 \left (4+e^5\right )^3}+\frac {\int e^{x/4} x^2 \, dx}{4 \left (4+e^5\right )^2}+\frac {(12+\log (9)) \int e^{x/4} x \, dx}{4 \left (4+e^5\right )^2}+\frac {\left (80+e^5 \left (18+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right ) \int e^{x/4} \, dx}{4 \left (4+e^5\right )^3}\\ &=\frac {e^{x/4} x^2}{\left (4+e^5\right )^2}-\frac {3 x^4 (2+x+\log (3))^2}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {e^{x/4} x (12+\log (9))}{\left (4+e^5\right )^2}+\frac {e^{x/4} \left (80+e^5 \left (18+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right )}{\left (4+e^5\right )^3}+\frac {\int \left (\frac {e^{x/4} \left (-2 e^5 \sqrt {4+e^5} (4+\log (9))+i e^{5/2} \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )+\log (3) (32-3 \log (81))\right )\right )}{2 \left (i e^{5/2}+\sqrt {4+e^5} x\right )}+\frac {e^{x/4} \left (2 e^5 \sqrt {4+e^5} (4+\log (9))+i e^{5/2} \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )+\log (3) (32-3 \log (81))\right )\right )}{2 \left (i e^{5/2}-\sqrt {4+e^5} x\right )}\right ) \, dx}{4 \left (4+e^5\right )^3}+\frac {\int \left (\frac {e^{5+\frac {x}{4}} \left (4+e^5\right ) x \left (64 (2+\log (3))^2+e^5 \left (44+64 \log (3)+16 \log ^2(3)+\log (9)\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}+\frac {e^{10+\frac {x}{4}} \left (-432-208 \log (3)-8 \log ^2(3)-e^5 \left (109+52 \log (3)-\log ^2(3)\right )+\log (27) \log (81)\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}\right ) \, dx}{4 \left (4+e^5\right )^3}+\frac {\int \left (\frac {e^{15+\frac {x}{4}} \left (256+4 \log ^2(3)+32 e^5 (2+\log (3))+\log (3) (128-\log (81))\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3}+\frac {16 e^{10+\frac {x}{4}} x \left (-16 (2+\log (3))^2-4 e^5 \left (7+8 \log (3)+2 \log ^2(3)\right )-e^{10} \left (3+\log ^2(3)+\log (81)\right )\right )}{\left (e^5+\left (4+e^5\right ) x^2\right )^3}\right ) \, dx}{4 \left (4+e^5\right )^3}-\frac {2 \int e^{x/4} x \, dx}{\left (4+e^5\right )^2}-\frac {(12+\log (9)) \int e^{x/4} \, dx}{\left (4+e^5\right )^2}\\ &=-\frac {8 e^{x/4} x}{\left (4+e^5\right )^2}+\frac {e^{x/4} x^2}{\left (4+e^5\right )^2}-\frac {3 x^4 (2+x+\log (3))^2}{\left (e^5+\left (4+e^5\right ) x^2\right )^2}-\frac {4 e^{x/4} (12+\log (9))}{\left (4+e^5\right )^2}+\frac {e^{x/4} x (12+\log (9))}{\left (4+e^5\right )^2}+\frac {e^{x/4} \left (80+e^5 \left (18+12 \log (3)+\log ^2(3)\right )+\log (3) (48+\log (81))\right )}{\left (4+e^5\right )^3}+\frac {8 \int e^{x/4} \, dx}{\left (4+e^5\right )^2}+\frac {\left (64 (2+\log (3))^2+e^5 \left (44+64 \log (3)+16 \log ^2(3)+\log (9)\right )\right ) \int \frac {e^{5+\frac {x}{4}} x}{\left (e^5+\left (4+e^5\right ) x^2\right )^2} \, dx}{4 \left (4+e^5\right )^2}-\frac {\left (e^{5/2} \left (2 e^{5/2} \sqrt {4+e^5} (4+\log (9))-i \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )+\log (3) (32-3 \log (81))\right )\right )\right ) \int \frac {e^{x/4}}{i e^{5/2}+\sqrt {4+e^5} x} \, dx}{8 \left (4+e^5\right )^3}+\frac {\left (e^{5/2} \left (2 e^{5/2} \sqrt {4+e^5} (4+\log (9))+i \left (96+4 \log ^2(3)+e^5 \left (27+8 \log (3)-2 \log ^2(3)\right )+\log (3) (32-3 \log (81))\right )\right )\right ) \int \frac {e^{x/4}}{i e^{5/2}-\sqrt {4+e^5} x} \, dx}{8 \left (4+e^5\right )^3}+\frac {\left (256+4 \log ^2(3)+32 e^5 (2+\log (3))+\log (3) (128-\log (81))\right ) \int \frac {e^{15+\frac {x}{4}}}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx}{4 \left (4+e^5\right )^3}-\frac {\left (432+208 \log (3)+8 \log ^2(3)+e^5 \left (109+52 \log (3)-\log ^2(3)\right )-\log (27) \log (81)\right ) \int \frac {e^{10+\frac {x}{4}}}{\left (e^5+\left (4+e^5\right ) x^2\right )^2} \, dx}{4 \left (4+e^5\right )^3}-\frac {\left (4 \left (16 (2+\log (3))^2+4 e^5 \left (7+8 \log (3)+2 \log ^2(3)\right )+e^{10} \left (3+\log ^2(3)+\log (81)\right )\right )\right ) \int \frac {e^{10+\frac {x}{4}} x}{\left (e^5+\left (4+e^5\right ) x^2\right )^3} \, dx}{\left (4+e^5\right )^3}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] time = 0.38, size = 265, normalized size = 8.55 \begin {gather*} \frac {192 e^{5+\frac {x}{4}} x^4 (2+x+\log (3))^2+48 e^{10+\frac {x}{4}} x^4 (2+x+\log (3))^2+4 e^{15+\frac {x}{4}} x^4 (2+x+\log (3))^2+256 e^{x/4} x^4 (2+x+\log (3))^2-768 x^5 (4+x+\log (9))-3 e^{15} \left (8 x^4+4 x^6-\log ^2(9)-2 (4+\log (6561))+x^5 (16+\log (6561))-x^2 (\log (9) \log (81)+2 (8+\log (43046721)))\right )-48 e^5 x^2 \left (8 x^2+12 x^4-\log (9) \log (81)-2 (16+\log (43046721))+x^3 (48+\log (282429536481))\right )-12 e^{10} \left (16 x^4+12 x^6-\log ^2(9)-2 (8+\log (6561))+x^5 (48+\log (282429536481))-x^2 (48+\log (9) \log (6561)+2 \log (1853020188851841))\right )}{4 \left (4+e^5\right )^3 \left (4 x^2+e^5 \left (1+x^2\right )\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-192*x^6 - 96*x^7 + E^5*(-192*x^3 - 240*x^4 - 72*x^5 - 48*x^6 - 24*x^7) + (-96*x^6 + E^5*(-192*x^3

- 120*x^4 - 24*x^6))*Log[3] - 48*E^5*x^3*Log[3]^2 + E^(x/4)*(80*x^6 + 48*x^7 + 4*x^8 + E^5*(64*x^3 + 84*x^4 +

28*x^5 + 21*x^6 + 12*x^7 + x^8) + (48*x^6 + 8*x^7 + E^5*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7))*Log[3] + (

4*x^6 + E^5*(16*x^3 + x^4 + x^6))*Log[3]^2))/(256*x^6 + E^15*(4 + 12*x^2 + 12*x^4 + 4*x^6) + E^10*(48*x^2 + 96

*x^4 + 48*x^6) + E^5*(192*x^4 + 192*x^6)),x]

[Out]

(192*E^(5 + x/4)*x^4*(2 + x + Log[3])^2 + 48*E^(10 + x/4)*x^4*(2 + x + Log[3])^2 + 4*E^(15 + x/4)*x^4*(2 + x +

Log[3])^2 + 256*E^(x/4)*x^4*(2 + x + Log[3])^2 - 768*x^5*(4 + x + Log[9]) - 3*E^15*(8*x^4 + 4*x^6 - Log[9]^2

- 2*(4 + Log[6561]) + x^5*(16 + Log[6561]) - x^2*(Log[9]*Log[81] + 2*(8 + Log[43046721]))) - 48*E^5*x^2*(8*x^2

+ 12*x^4 - Log[9]*Log[81] - 2*(16 + Log[43046721]) + x^3*(48 + Log[282429536481])) - 12*E^10*(16*x^4 + 12*x^6

- Log[9]^2 - 2*(8 + Log[6561]) + x^5*(48 + Log[282429536481]) - x^2*(48 + Log[9]*Log[6561] + 2*Log[1853020188

851841])))/(4*(4 + E^5)^3*(4*x^2 + E^5*(1 + x^2))^2)

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fricas [B] time = 1.01, size = 420, normalized size = 13.55 \begin {gather*} -\frac {192 \, x^{6} + 768 \, x^{5} - 3 \, {\left (32 \, x^{2} e^{5} + {\left (2 \, x^{2} + 1\right )} e^{15} + 4 \, {\left (4 \, x^{2} + 1\right )} e^{10}\right )} \log \relax (3)^{2} + 3 \, {\left (x^{6} + 4 \, x^{5} + 2 \, x^{4} - 4 \, x^{2} - 2\right )} e^{15} + 12 \, {\left (3 \, x^{6} + 12 \, x^{5} + 4 \, x^{4} - 12 \, x^{2} - 4\right )} e^{10} + 48 \, {\left (3 \, x^{6} + 12 \, x^{5} + 2 \, x^{4} - 8 \, x^{2}\right )} e^{5} - {\left (64 \, x^{6} + 256 \, x^{5} + 256 \, x^{4} + {\left (x^{4} e^{15} + 12 \, x^{4} e^{10} + 48 \, x^{4} e^{5} + 64 \, x^{4}\right )} \log \relax (3)^{2} + {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{15} + 12 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{10} + 48 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{5} + 2 \, {\left (64 \, x^{5} + 128 \, x^{4} + {\left (x^{5} + 2 \, x^{4}\right )} e^{15} + 12 \, {\left (x^{5} + 2 \, x^{4}\right )} e^{10} + 48 \, {\left (x^{5} + 2 \, x^{4}\right )} e^{5}\right )} \log \relax (3)\right )} e^{\left (\frac {1}{4} \, x\right )} + 6 \, {\left (64 \, x^{5} + {\left (x^{5} - 4 \, x^{2} - 2\right )} e^{15} + 4 \, {\left (3 \, x^{5} - 8 \, x^{2} - 2\right )} e^{10} + 16 \, {\left (3 \, x^{5} - 4 \, x^{2}\right )} e^{5}\right )} \log \relax (3)}{1024 \, x^{4} + {\left (x^{4} + 2 \, x^{2} + 1\right )} e^{25} + 4 \, {\left (5 \, x^{4} + 8 \, x^{2} + 3\right )} e^{20} + 16 \, {\left (10 \, x^{4} + 12 \, x^{2} + 3\right )} e^{15} + 64 \, {\left (10 \, x^{4} + 8 \, x^{2} + 1\right )} e^{10} + 256 \, {\left (5 \, x^{4} + 2 \, x^{2}\right )} e^{5}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*

log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+

((-24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-192*x^3)*exp(5)-96*x^7-192*x^6

)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algor

ithm="fricas")

[Out]

-(192*x^6 + 768*x^5 - 3*(32*x^2*e^5 + (2*x^2 + 1)*e^15 + 4*(4*x^2 + 1)*e^10)*log(3)^2 + 3*(x^6 + 4*x^5 + 2*x^4

- 4*x^2 - 2)*e^15 + 12*(3*x^6 + 12*x^5 + 4*x^4 - 12*x^2 - 4)*e^10 + 48*(3*x^6 + 12*x^5 + 2*x^4 - 8*x^2)*e^5 -

(64*x^6 + 256*x^5 + 256*x^4 + (x^4*e^15 + 12*x^4*e^10 + 48*x^4*e^5 + 64*x^4)*log(3)^2 + (x^6 + 4*x^5 + 4*x^4)

*e^15 + 12*(x^6 + 4*x^5 + 4*x^4)*e^10 + 48*(x^6 + 4*x^5 + 4*x^4)*e^5 + 2*(64*x^5 + 128*x^4 + (x^5 + 2*x^4)*e^1

5 + 12*(x^5 + 2*x^4)*e^10 + 48*(x^5 + 2*x^4)*e^5)*log(3))*e^(1/4*x) + 6*(64*x^5 + (x^5 - 4*x^2 - 2)*e^15 + 4*(

3*x^5 - 8*x^2 - 2)*e^10 + 16*(3*x^5 - 4*x^2)*e^5)*log(3))/(1024*x^4 + (x^4 + 2*x^2 + 1)*e^25 + 4*(5*x^4 + 8*x^

2 + 3)*e^20 + 16*(10*x^4 + 12*x^2 + 3)*e^15 + 64*(10*x^4 + 8*x^2 + 1)*e^10 + 256*(5*x^4 + 2*x^2)*e^5)

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giac [B] time = 0.93, size = 2810, normalized size = 90.65 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*

log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+

((-24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-192*x^3)*exp(5)-96*x^7-192*x^6

)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algor

ithm="giac")

[Out]

-(3*x^6*e^45 + 108*x^6*e^40 + 1728*x^6*e^35 + 16128*x^6*e^30 + 96768*x^6*e^25 + 387072*x^6*e^20 + 1032192*x^6*

e^15 + 1769472*x^6*e^10 + 1769472*x^6*e^5 - 262144*x^6*e^(1/4*x) - x^6*e^(1/4*x + 45) - 36*x^6*e^(1/4*x + 40)

- 576*x^6*e^(1/4*x + 35) - 5376*x^6*e^(1/4*x + 30) - 32256*x^6*e^(1/4*x + 25) - 129024*x^6*e^(1/4*x + 20) - 34

4064*x^6*e^(1/4*x + 15) - 589824*x^6*e^(1/4*x + 10) - 589824*x^6*e^(1/4*x + 5) + 6*x^5*e^45*log(3) + 216*x^5*e

^40*log(3) + 3456*x^5*e^35*log(3) + 32256*x^5*e^30*log(3) + 193536*x^5*e^25*log(3) + 774144*x^5*e^20*log(3) +

2064384*x^5*e^15*log(3) + 3538944*x^5*e^10*log(3) + 3538944*x^5*e^5*log(3) - 524288*x^5*e^(1/4*x)*log(3) - 2*x

^5*e^(1/4*x + 45)*log(3) - 72*x^5*e^(1/4*x + 40)*log(3) - 1152*x^5*e^(1/4*x + 35)*log(3) - 10752*x^5*e^(1/4*x

+ 30)*log(3) - 64512*x^5*e^(1/4*x + 25)*log(3) - 258048*x^5*e^(1/4*x + 20)*log(3) - 688128*x^5*e^(1/4*x + 15)*

log(3) - 1179648*x^5*e^(1/4*x + 10)*log(3) - 1179648*x^5*e^(1/4*x + 5)*log(3) - 262144*x^4*e^(1/4*x)*log(3)^2

- x^4*e^(1/4*x + 45)*log(3)^2 - 36*x^4*e^(1/4*x + 40)*log(3)^2 - 576*x^4*e^(1/4*x + 35)*log(3)^2 - 5376*x^4*e^

(1/4*x + 30)*log(3)^2 - 32256*x^4*e^(1/4*x + 25)*log(3)^2 - 129024*x^4*e^(1/4*x + 20)*log(3)^2 - 344064*x^4*e^

(1/4*x + 15)*log(3)^2 - 589824*x^4*e^(1/4*x + 10)*log(3)^2 - 589824*x^4*e^(1/4*x + 5)*log(3)^2 + 786432*x^6 +

12*x^5*e^45 + 432*x^5*e^40 + 6912*x^5*e^35 + 64512*x^5*e^30 + 387072*x^5*e^25 + 1548288*x^5*e^20 + 4128768*x^5

*e^15 + 7077888*x^5*e^10 + 7077888*x^5*e^5 - 1048576*x^5*e^(1/4*x) - 4*x^5*e^(1/4*x + 45) - 144*x^5*e^(1/4*x +

40) - 2304*x^5*e^(1/4*x + 35) - 21504*x^5*e^(1/4*x + 30) - 129024*x^5*e^(1/4*x + 25) - 516096*x^5*e^(1/4*x +

20) - 1376256*x^5*e^(1/4*x + 15) - 2359296*x^5*e^(1/4*x + 10) - 2359296*x^5*e^(1/4*x + 5) + 1572864*x^5*log(3)

- 1048576*x^4*e^(1/4*x)*log(3) - 4*x^4*e^(1/4*x + 45)*log(3) - 144*x^4*e^(1/4*x + 40)*log(3) - 2304*x^4*e^(1/

4*x + 35)*log(3) - 21504*x^4*e^(1/4*x + 30)*log(3) - 129024*x^4*e^(1/4*x + 25)*log(3) - 516096*x^4*e^(1/4*x +

20)*log(3) - 1376256*x^4*e^(1/4*x + 15)*log(3) - 2359296*x^4*e^(1/4*x + 10)*log(3) - 2359296*x^4*e^(1/4*x + 5)

*log(3) + 3145728*x^5 + 6*x^4*e^45 + 192*x^4*e^40 + 2688*x^4*e^35 + 21504*x^4*e^30 + 107520*x^4*e^25 + 344064*

x^4*e^20 + 688128*x^4*e^15 + 786432*x^4*e^10 + 393216*x^4*e^5 - 1048576*x^4*e^(1/4*x) - 4*x^4*e^(1/4*x + 45) -

144*x^4*e^(1/4*x + 40) - 2304*x^4*e^(1/4*x + 35) - 21504*x^4*e^(1/4*x + 30) - 129024*x^4*e^(1/4*x + 25) - 516

096*x^4*e^(1/4*x + 20) - 1376256*x^4*e^(1/4*x + 15) - 2359296*x^4*e^(1/4*x + 10) - 2359296*x^4*e^(1/4*x + 5) -

12*x^3*e^45*log(3) - 384*x^3*e^40*log(3) - 5376*x^3*e^35*log(3) - 43008*x^3*e^30*log(3) - 215040*x^3*e^25*log

(3) - 688128*x^3*e^20*log(3) - 1376256*x^3*e^15*log(3) - 1572864*x^3*e^10*log(3) - 786432*x^3*e^5*log(3) + 4*x

^3*e^(1/4*x + 45)*log(3) + 128*x^3*e^(1/4*x + 40)*log(3) + 1792*x^3*e^(1/4*x + 35)*log(3) + 14336*x^3*e^(1/4*x

+ 30)*log(3) + 71680*x^3*e^(1/4*x + 25)*log(3) + 229376*x^3*e^(1/4*x + 20)*log(3) + 458752*x^3*e^(1/4*x + 15)

*log(3) + 524288*x^3*e^(1/4*x + 10)*log(3) + 262144*x^3*e^(1/4*x + 5)*log(3) - 12*x^2*e^45*log(3)^2 - 384*x^2*

e^40*log(3)^2 - 5376*x^2*e^35*log(3)^2 - 43008*x^2*e^30*log(3)^2 - 215040*x^2*e^25*log(3)^2 - 688128*x^2*e^20*

log(3)^2 - 1376256*x^2*e^15*log(3)^2 - 1572864*x^2*e^10*log(3)^2 - 786432*x^2*e^5*log(3)^2 + 2*x^2*e^(1/4*x +

45)*log(3)^2 + 64*x^2*e^(1/4*x + 40)*log(3)^2 + 896*x^2*e^(1/4*x + 35)*log(3)^2 + 7168*x^2*e^(1/4*x + 30)*log(

3)^2 + 35840*x^2*e^(1/4*x + 25)*log(3)^2 + 114688*x^2*e^(1/4*x + 20)*log(3)^2 + 229376*x^2*e^(1/4*x + 15)*log(

3)^2 + 262144*x^2*e^(1/4*x + 10)*log(3)^2 + 131072*x^2*e^(1/4*x + 5)*log(3)^2 - 24*x^3*e^45 - 768*x^3*e^40 - 1

0752*x^3*e^35 - 86016*x^3*e^30 - 430080*x^3*e^25 - 1376256*x^3*e^20 - 2752512*x^3*e^15 - 3145728*x^3*e^10 - 15

72864*x^3*e^5 + 8*x^3*e^(1/4*x + 45) + 256*x^3*e^(1/4*x + 40) + 3584*x^3*e^(1/4*x + 35) + 28672*x^3*e^(1/4*x +

30) + 143360*x^3*e^(1/4*x + 25) + 458752*x^3*e^(1/4*x + 20) + 917504*x^3*e^(1/4*x + 15) + 1048576*x^3*e^(1/4*

x + 10) + 524288*x^3*e^(1/4*x + 5) - 48*x^2*e^45*log(3) - 1536*x^2*e^40*log(3) - 21504*x^2*e^35*log(3) - 17203

2*x^2*e^30*log(3) - 860160*x^2*e^25*log(3) - 2752512*x^2*e^20*log(3) - 5505024*x^2*e^15*log(3) - 6291456*x^2*e

^10*log(3) - 3145728*x^2*e^5*log(3) + 8*x^2*e^(1/4*x + 45)*log(3) + 256*x^2*e^(1/4*x + 40)*log(3) + 3584*x^2*e

^(1/4*x + 35)*log(3) + 28672*x^2*e^(1/4*x + 30)*log(3) + 143360*x^2*e^(1/4*x + 25)*log(3) + 458752*x^2*e^(1/4*

x + 20)*log(3) + 917504*x^2*e^(1/4*x + 15)*log(3) + 1048576*x^2*e^(1/4*x + 10)*log(3) + 524288*x^2*e^(1/4*x +

5)*log(3) - 27*x^2*e^45 - 948*x^2*e^40 - 14448*x^2*e^35 - 124992*x^2*e^30 - 672000*x^2*e^25 - 2300928*x^2*e^20

- 4902912*x^2*e^15 - 5947392*x^2*e^10 - 3145728*x^2*e^5 + 5*x^2*e^(1/4*x + 45) + 172*x^2*e^(1/4*x + 40) + 257

6*x^2*e^(1/4*x + 35) + 21952*x^2*e^(1/4*x + 30) + 116480*x^2*e^(1/4*x + 25) + 394240*x^2*e^(1/4*x + 20) + 8314

88*x^2*e^(1/4*x + 15) + 999424*x^2*e^(1/4*x + 10) + 524288*x^2*e^(1/4*x + 5) - 6*x*e^45*log(3) - 168*x*e^40*lo

g(3) - 2016*x*e^35*log(3) - 13440*x*e^30*log(3) - 53760*x*e^25*log(3) - 129024*x*e^20*log(3) - 172032*x*e^15*l

og(3) - 98304*x*e^10*log(3) + 2*x*e^(1/4*x + 45)*log(3) + 56*x*e^(1/4*x + 40)*log(3) + 672*x*e^(1/4*x + 35)*lo

g(3) + 4480*x*e^(1/4*x + 30)*log(3) + 17920*x*e^(1/4*x + 25)*log(3) + 43008*x*e^(1/4*x + 20)*log(3) + 57344*x*

e^(1/4*x + 15)*log(3) + 32768*x*e^(1/4*x + 10)*log(3) - 6*e^45*log(3)^2 - 168*e^40*log(3)^2 - 2016*e^35*log(3)

^2 - 13440*e^30*log(3)^2 - 53760*e^25*log(3)^2 - 129024*e^20*log(3)^2 - 172032*e^15*log(3)^2 - 98304*e^10*log(

3)^2 + e^(1/4*x + 45)*log(3)^2 + 28*e^(1/4*x + 40)*log(3)^2 + 336*e^(1/4*x + 35)*log(3)^2 + 2240*e^(1/4*x + 30

)*log(3)^2 + 8960*e^(1/4*x + 25)*log(3)^2 + 21504*e^(1/4*x + 20)*log(3)^2 + 28672*e^(1/4*x + 15)*log(3)^2 + 16

384*e^(1/4*x + 10)*log(3)^2 - 12*x*e^45 - 336*x*e^40 - 4032*x*e^35 - 26880*x*e^30 - 107520*x*e^25 - 258048*x*e

^20 - 344064*x*e^15 - 196608*x*e^10 + 4*x*e^(1/4*x + 45) + 112*x*e^(1/4*x + 40) + 1344*x*e^(1/4*x + 35) + 8960

*x*e^(1/4*x + 30) + 35840*x*e^(1/4*x + 25) + 86016*x*e^(1/4*x + 20) + 114688*x*e^(1/4*x + 15) + 65536*x*e^(1/4

*x + 10) - 24*e^45*log(3) - 672*e^40*log(3) - 8064*e^35*log(3) - 53760*e^30*log(3) - 215040*e^25*log(3) - 5160

96*e^20*log(3) - 688128*e^15*log(3) - 393216*e^10*log(3) + 4*e^(1/4*x + 45)*log(3) + 112*e^(1/4*x + 40)*log(3)

+ 1344*e^(1/4*x + 35)*log(3) + 8960*e^(1/4*x + 30)*log(3) + 35840*e^(1/4*x + 25)*log(3) + 86016*e^(1/4*x + 20

)*log(3) + 114688*e^(1/4*x + 15)*log(3) + 65536*e^(1/4*x + 10)*log(3) - 12*e^45 - 384*e^40 - 5184*e^35 - 38400

*e^30 - 168960*e^25 - 442368*e^20 - 638976*e^15 - 393216*e^10 + 2*e^(1/4*x + 45) + 64*e^(1/4*x + 40) + 864*e^(

1/4*x + 35) + 6400*e^(1/4*x + 30) + 28160*e^(1/4*x + 25) + 73728*e^(1/4*x + 20) + 106496*e^(1/4*x + 15) + 6553

6*e^(1/4*x + 10))/(x^4*e^55 + 44*x^4*e^50 + 880*x^4*e^45 + 10560*x^4*e^40 + 84480*x^4*e^35 + 473088*x^4*e^30 +

1892352*x^4*e^25 + 5406720*x^4*e^20 + 10813440*x^4*e^15 + 14417920*x^4*e^10 + 11534336*x^4*e^5 + 4194304*x^4

+ 2*x^2*e^55 + 80*x^2*e^50 + 1440*x^2*e^45 + 15360*x^2*e^40 + 107520*x^2*e^35 + 516096*x^2*e^30 + 1720320*x^2*

e^25 + 3932160*x^2*e^20 + 5898240*x^2*e^15 + 5242880*x^2*e^10 + 2097152*x^2*e^5 + e^55 + 36*e^50 + 576*e^45 +

5376*e^40 + 32256*e^35 + 129024*e^30 + 344064*e^25 + 589824*e^20 + 589824*e^15 + 262144*e^10)

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maple [B] time = 0.91, size = 90, normalized size = 2.90


method	result	size

norman	\(\frac {\left (-6 \ln \relax (3)-12\right ) x^{5}+\left (-3 \ln \relax (3)^{2}-12 \ln \relax (3)-12\right ) x^{4}+{\mathrm e}^{\frac {x}{4}} x^{6}+\left (2 \ln \relax (3)+4\right ) x^{5} {\mathrm e}^{\frac {x}{4}}+\left (\ln \relax (3)^{2}+4 \ln \relax (3)+4\right ) x^{4} {\mathrm e}^{\frac {x}{4}}-3 x^{6}}{\left (x^{2} {\mathrm e}^{5}+4 x^{2}+{\mathrm e}^{5}\right )^{2}}\)	\(90\)
risch	\(-\frac {6 \ln \relax (3) x}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}-\frac {3 x^{2}}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}-\frac {12 x}{{\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16}+\frac {12 \,{\mathrm e}^{5} \left ({\mathrm e}^{5} \ln \relax (3)+2 \,{\mathrm e}^{5}+4 \ln \relax (3)+8\right ) x^{3}+3 \left (2 \,{\mathrm e}^{5} \ln \relax (3)^{2}+8 \,{\mathrm e}^{5} \ln \relax (3)+8 \ln \relax (3)^{2}+5 \,{\mathrm e}^{5}+32 \ln \relax (3)+32\right ) {\mathrm e}^{5} x^{2}+\left (6 \,{\mathrm e}^{10} \ln \relax (3)+12 \,{\mathrm e}^{10}\right ) x +\frac {3 \,{\mathrm e}^{10} \left ({\mathrm e}^{5} \ln \relax (3)^{2}+4 \,{\mathrm e}^{5} \ln \relax (3)+4 \ln \relax (3)^{2}+2 \,{\mathrm e}^{5}+16 \ln \relax (3)+16\right )}{4+{\mathrm e}^{5}}}{\left ({\mathrm e}^{10}+8 \,{\mathrm e}^{5}+16\right ) \left (x^{4} {\mathrm e}^{10}+8 x^{4} {\mathrm e}^{5}+2 x^{2} {\mathrm e}^{10}+16 x^{4}+8 x^{2} {\mathrm e}^{5}+{\mathrm e}^{10}\right )}+\frac {\left (\ln \relax (3)^{2}+2 x \ln \relax (3)+x^{2}+4 \ln \relax (3)+4 x +4\right ) x^{4} {\mathrm e}^{\frac {x}{4}}}{\left (x^{2} {\mathrm e}^{5}+4 x^{2}+{\mathrm e}^{5}\right )^{2}}\)	\(250\)
derivativedivides	\(\text {Expression too large to display}\)	\(16028\)
default	\(\text {Expression too large to display}\)	\(16028\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*ln(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*ln(3)+(

x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*ln(3)^2+((-24*x^6

-120*x^4-192*x^3)*exp(5)-96*x^6)*ln(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-192*x^3)*exp(5)-96*x^7-192*x^6)/((4*x^6+

12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x,method=_RETURNVE

RBOSE)

[Out]

((-6*ln(3)-12)*x^5+(-3*ln(3)^2-12*ln(3)-12)*x^4+exp(1/4*x)*x^6+(2*ln(3)+4)*x^5*exp(1/4*x)+(ln(3)^2+4*ln(3)+4)*

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

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maxima [B] time = 0.59, size = 1473, normalized size = 47.52 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x^6+x^4+16*x^3)*exp(5)+4*x^6)*log(3)^2+((2*x^7+12*x^6+2*x^5+44*x^4+64*x^3)*exp(5)+8*x^7+48*x^6)*

log(3)+(x^8+12*x^7+21*x^6+28*x^5+84*x^4+64*x^3)*exp(5)+4*x^8+48*x^7+80*x^6)*exp(1/4*x)-48*x^3*exp(5)*log(3)^2+

((-24*x^6-120*x^4-192*x^3)*exp(5)-96*x^6)*log(3)+(-24*x^7-48*x^6-72*x^5-240*x^4-192*x^3)*exp(5)-96*x^7-192*x^6

)/((4*x^6+12*x^4+12*x^2+4)*exp(5)^3+(48*x^6+96*x^4+48*x^2)*exp(5)^2+(192*x^6+192*x^4)*exp(5)+256*x^6),x, algor

ithm="maxima")

[Out]

3/4*(15*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(5/2)/((e^15 + 12*e^10 + 48*e^5 + 64)*sqrt(e^5 + 4)) - (9*x^3*(e^10

+ 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20*e^20 + 160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 +

96*e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^20 + 48*e^15 + 64*e^10) - 8*x/(e^15 + 12*e^10 + 48*e^5 + 64))*e^5*

log(3) - 15/4*(3*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(-5/2)/((e^10 + 8*e^5 + 16)*sqrt(e^5 + 4)) - (5*x^3*(e^5 +

4) + 3*x*e^5)/(x^4*(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e

^20 + 8*e^15 + 16*e^10))*e^5*log(3) + 3*(2*x^2*(e^5 + 4) + e^5)*e^5*log(3)^2/(x^4*(e^20 + 16*e^15 + 96*e^10 +

256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20 + 8*e^15 + 16*e^10) - 3/2*(2*x^2/(e^15 + 12*

e^10 + 48*e^5 + 64) - 6*e^5*log(x^2*(e^5 + 4) + e^5)/(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) - (6*x^2*(e^15

+ 4*e^10) + 5*e^15)/(x^4*(e^30 + 24*e^25 + 240*e^20 + 1280*e^15 + 3840*e^10 + 6144*e^5 + 4096) + 2*x^2*(e^30

+ 20*e^25 + 160*e^20 + 640*e^15 + 1280*e^10 + 1024*e^5) + e^30 + 16*e^25 + 96*e^20 + 256*e^15 + 256*e^10))*e^5

+ 3/2*(15*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(5/2)/((e^15 + 12*e^10 + 48*e^5 + 64)*sqrt(e^5 + 4)) - (9*x^3*(e

^10 + 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20*e^20 + 160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20

+ 96*e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^20 + 48*e^15 + 64*e^10) - 8*x/(e^15 + 12*e^10 + 48*e^5 + 64))*e

^5 - 15/2*(3*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(-5/2)/((e^10 + 8*e^5 + 16)*sqrt(e^5 + 4)) - (5*x^3*(e^5 + 4)

+ 3*x*e^5)/(x^4*(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20

+ 8*e^15 + 16*e^10))*e^5 - 9/2*((4*x^2*(e^10 + 4*e^5) + 3*e^10)/(x^4*(e^25 + 20*e^20 + 160*e^15 + 640*e^10 + 1

280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 + 96*e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^20 + 48*e^15 + 64*e^10)

+ 2*log(x^2*(e^5 + 4) + e^5)/(e^15 + 12*e^10 + 48*e^5 + 64))*e^5 + 3*(15*arctan(x*sqrt(e^5 + 4)*e^(-5/2))*e^(5

/2)/((e^15 + 12*e^10 + 48*e^5 + 64)*sqrt(e^5 + 4)) - (9*x^3*(e^10 + 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20*e^20 +

160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 + 96*e^15 + 256*e^10 + 256*e^5) + e^25 + 12*e^2

0 + 48*e^15 + 64*e^10) - 8*x/(e^15 + 12*e^10 + 48*e^5 + 64))*log(3) + 12*(2*x^2*(e^5 + 4) + e^5)*e^5*log(3)/(x

^4*(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20 + 8*e^15 + 16

*e^10) - 12*x^2/(e^15 + 12*e^10 + 48*e^5 + 64) + 12*(2*x^2*(e^5 + 4) + e^5)*e^5/(x^4*(e^20 + 16*e^15 + 96*e^10

+ 256*e^5 + 256) + 2*x^2*(e^20 + 12*e^15 + 48*e^10 + 64*e^5) + e^20 + 8*e^15 + 16*e^10) + (x^6 + 2*x^5*(log(3

) + 2) + (log(3)^2 + 4*log(3) + 4)*x^4)*e^(1/4*x)/(x^4*(e^10 + 8*e^5 + 16) + 2*x^2*(e^10 + 4*e^5) + e^10) + 36

*e^5*log(x^2*(e^5 + 4) + e^5)/(e^20 + 16*e^15 + 96*e^10 + 256*e^5 + 256) + 90*arctan(x*sqrt(e^5 + 4)*e^(-5/2))

*e^(5/2)/((e^15 + 12*e^10 + 48*e^5 + 64)*sqrt(e^5 + 4)) - 6*(9*x^3*(e^10 + 4*e^5) + 7*x*e^10)/(x^4*(e^25 + 20*

e^20 + 160*e^15 + 640*e^10 + 1280*e^5 + 1024) + 2*x^2*(e^25 + 16*e^20 + 96*e^15 + 256*e^10 + 256*e^5) + e^25 +

12*e^20 + 48*e^15 + 64*e^10) + 6*(6*x^2*(e^15 + 4*e^10) + 5*e^15)/(x^4*(e^30 + 24*e^25 + 240*e^20 + 1280*e^15

+ 3840*e^10 + 6144*e^5 + 4096) + 2*x^2*(e^30 + 20*e^25 + 160*e^20 + 640*e^15 + 1280*e^10 + 1024*e^5) + e^30 +

16*e^25 + 96*e^20 + 256*e^15 + 256*e^10) - 48*x/(e^15 + 12*e^10 + 48*e^5 + 64)

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {\ln \relax (3)\,\left ({\mathrm {e}}^5\,\left (24\,x^6+120\,x^4+192\,x^3\right )+96\,x^6\right )+{\mathrm {e}}^5\,\left (24\,x^7+48\,x^6+72\,x^5+240\,x^4+192\,x^3\right )-{\mathrm {e}}^{x/4}\,\left ({\mathrm {e}}^5\,\left (x^8+12\,x^7+21\,x^6+28\,x^5+84\,x^4+64\,x^3\right )+{\ln \relax (3)}^2\,\left ({\mathrm {e}}^5\,\left (x^6+x^4+16\,x^3\right )+4\,x^6\right )+\ln \relax (3)\,\left ({\mathrm {e}}^5\,\left (2\,x^7+12\,x^6+2\,x^5+44\,x^4+64\,x^3\right )+48\,x^6+8\,x^7\right )+80\,x^6+48\,x^7+4\,x^8\right )+192\,x^6+96\,x^7+48\,x^3\,{\mathrm {e}}^5\,{\ln \relax (3)}^2}{{\mathrm {e}}^5\,\left (192\,x^6+192\,x^4\right )+{\mathrm {e}}^{15}\,\left (4\,x^6+12\,x^4+12\,x^2+4\right )+{\mathrm {e}}^{10}\,\left (48\,x^6+96\,x^4+48\,x^2\right )+256\,x^6} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(3)*(exp(5)*(192*x^3 + 120*x^4 + 24*x^6) + 96*x^6) + exp(5)*(192*x^3 + 240*x^4 + 72*x^5 + 48*x^6 + 24

*x^7) - exp(x/4)*(exp(5)*(64*x^3 + 84*x^4 + 28*x^5 + 21*x^6 + 12*x^7 + x^8) + log(3)^2*(exp(5)*(16*x^3 + x^4 +

x^6) + 4*x^6) + log(3)*(exp(5)*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7) + 48*x^6 + 8*x^7) + 80*x^6 + 48*x^7

+ 4*x^8) + 192*x^6 + 96*x^7 + 48*x^3*exp(5)*log(3)^2)/(exp(5)*(192*x^4 + 192*x^6) + exp(15)*(12*x^2 + 12*x^4

+ 4*x^6 + 4) + exp(10)*(48*x^2 + 96*x^4 + 48*x^6) + 256*x^6),x)

[Out]

-int((log(3)*(exp(5)*(192*x^3 + 120*x^4 + 24*x^6) + 96*x^6) + exp(5)*(192*x^3 + 240*x^4 + 72*x^5 + 48*x^6 + 24

*x^7) - exp(x/4)*(exp(5)*(64*x^3 + 84*x^4 + 28*x^5 + 21*x^6 + 12*x^7 + x^8) + log(3)^2*(exp(5)*(16*x^3 + x^4 +

x^6) + 4*x^6) + log(3)*(exp(5)*(64*x^3 + 44*x^4 + 2*x^5 + 12*x^6 + 2*x^7) + 48*x^6 + 8*x^7) + 80*x^6 + 48*x^7

+ 4*x^8) + 192*x^6 + 96*x^7 + 48*x^3*exp(5)*log(3)^2)/(exp(5)*(192*x^4 + 192*x^6) + exp(15)*(12*x^2 + 12*x^4

+ 4*x^6 + 4) + exp(10)*(48*x^2 + 96*x^4 + 48*x^6) + 256*x^6), x)

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sympy [B] time = 173.85, size = 405, normalized size = 13.06 \begin {gather*} - \frac {3 x^{2}}{16 + 8 e^{5} + e^{10}} - x \left (\frac {6 \log {\relax (3 )}}{16 + 8 e^{5} + e^{10}} + \frac {12}{16 + 8 e^{5} + e^{10}}\right ) - \frac {x^{3} \left (- 24 e^{15} - 12 e^{15} \log {\relax (3 )} - 192 e^{10} - 96 e^{10} \log {\relax (3 )} - 384 e^{5} - 192 e^{5} \log {\relax (3 )}\right ) + x^{2} \left (- 24 e^{15} \log {\relax (3 )} - 15 e^{15} - 6 e^{15} \log {\relax (3 )}^{2} - 192 e^{10} \log {\relax (3 )} - 156 e^{10} - 48 e^{10} \log {\relax (3 )}^{2} - 384 e^{5} \log {\relax (3 )} - 384 e^{5} - 96 e^{5} \log {\relax (3 )}^{2}\right ) + x \left (- 12 e^{15} - 6 e^{15} \log {\relax (3 )} - 48 e^{10} - 24 e^{10} \log {\relax (3 )}\right ) - 12 e^{15} \log {\relax (3 )} - 6 e^{15} - 3 e^{15} \log {\relax (3 )}^{2} - 48 e^{10} \log {\relax (3 )} - 48 e^{10} - 12 e^{10} \log {\relax (3 )}^{2}}{x^{4} \left (1024 + 1280 e^{5} + 640 e^{10} + 160 e^{15} + 20 e^{20} + e^{25}\right ) + x^{2} \left (512 e^{5} + 512 e^{10} + 192 e^{15} + 32 e^{20} + 2 e^{25}\right ) + 64 e^{10} + 48 e^{15} + 12 e^{20} + e^{25}} + \frac {\left (x^{6} + 2 x^{5} \log {\relax (3 )} + 4 x^{5} + x^{4} \log {\relax (3 )}^{2} + 4 x^{4} + 4 x^{4} \log {\relax (3 )}\right ) e^{\frac {x}{4}}}{16 x^{4} + 8 x^{4} e^{5} + x^{4} e^{10} + 8 x^{2} e^{5} + 2 x^{2} e^{10} + e^{10}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((x**6+x**4+16*x**3)*exp(5)+4*x**6)*ln(3)**2+((2*x**7+12*x**6+2*x**5+44*x**4+64*x**3)*exp(5)+8*x**

7+48*x**6)*ln(3)+(x**8+12*x**7+21*x**6+28*x**5+84*x**4+64*x**3)*exp(5)+4*x**8+48*x**7+80*x**6)*exp(1/4*x)-48*x

**3*exp(5)*ln(3)**2+((-24*x**6-120*x**4-192*x**3)*exp(5)-96*x**6)*ln(3)+(-24*x**7-48*x**6-72*x**5-240*x**4-192

*x**3)*exp(5)-96*x**7-192*x**6)/((4*x**6+12*x**4+12*x**2+4)*exp(5)**3+(48*x**6+96*x**4+48*x**2)*exp(5)**2+(192

*x**6+192*x**4)*exp(5)+256*x**6),x)

[Out]

-3*x**2/(16 + 8*exp(5) + exp(10)) - x*(6*log(3)/(16 + 8*exp(5) + exp(10)) + 12/(16 + 8*exp(5) + exp(10))) - (x

**3*(-24*exp(15) - 12*exp(15)*log(3) - 192*exp(10) - 96*exp(10)*log(3) - 384*exp(5) - 192*exp(5)*log(3)) + x**

2*(-24*exp(15)*log(3) - 15*exp(15) - 6*exp(15)*log(3)**2 - 192*exp(10)*log(3) - 156*exp(10) - 48*exp(10)*log(3

)**2 - 384*exp(5)*log(3) - 384*exp(5) - 96*exp(5)*log(3)**2) + x*(-12*exp(15) - 6*exp(15)*log(3) - 48*exp(10)

- 24*exp(10)*log(3)) - 12*exp(15)*log(3) - 6*exp(15) - 3*exp(15)*log(3)**2 - 48*exp(10)*log(3) - 48*exp(10) -

12*exp(10)*log(3)**2)/(x**4*(1024 + 1280*exp(5) + 640*exp(10) + 160*exp(15) + 20*exp(20) + exp(25)) + x**2*(51

2*exp(5) + 512*exp(10) + 192*exp(15) + 32*exp(20) + 2*exp(25)) + 64*exp(10) + 48*exp(15) + 12*exp(20) + exp(25

)) + (x**6 + 2*x**5*log(3) + 4*x**5 + x**4*log(3)**2 + 4*x**4 + 4*x**4*log(3))*exp(x/4)/(16*x**4 + 8*x**4*exp(

5) + x**4*exp(10) + 8*x**2*exp(5) + 2*x**2*exp(10) + exp(10))

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