3.59.22 \(\int \frac {8 e^8 x^5+72 x^6-32 x^7+(800 x^4+266 x^5-312 x^6+e^8 (32 x^3+42 x^4-8 x^5)) \log (2-x)+(3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 (52 x^3-26 x^4)) \log ^2(2-x)+(4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 (-256-80 x+104 x^2)) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} (-2 x^6+x^7)+e^{16} (-6 x^7+3 x^8)+e^8 (-6 x^8+3 x^9)+(-24 x^7-6 x^8+9 x^9+e^{24} (-24 x^4-6 x^5+9 x^6)+e^{16} (-72 x^5-18 x^6+27 x^7)+e^8 (-72 x^6-18 x^7+27 x^8)) \log (2-x)+(-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} (-96 x^2-96 x^3+18 x^4+27 x^5)+e^{16} (-288 x^3-288 x^4+54 x^5+81 x^6)+e^8 (-288 x^4-288 x^5+54 x^6+81 x^7)) \log ^2(2-x)+(-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} (-128-224 x-72 x^2+54 x^3+27 x^4)+e^{16} (-384 x-672 x^2-216 x^3+162 x^4+81 x^5)+e^8 (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6)) \log ^3(2-x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {\left (4+\frac {x}{4+3 x+\frac {x^2}{\log (2-x)}}\right )^2}{\left (e^8+x\right )^2} \]

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Rubi [F]  time = 22.10, 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 {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8*E^8*x^5 + 72*x^6 - 32*x^7 + (800*x^4 + 266*x^5 - 312*x^6 + E^8*(32*x^3 + 42*x^4 - 8*x^5))*Log[2 - x] +
(3072*x^2 + 3328*x^3 - 456*x^4 - 988*x^5 + E^8*(52*x^3 - 26*x^4))*Log[2 - x]^2 + (4096 + 7424*x + 2752*x^2 - 1
716*x^3 - 1014*x^4 + E^8*(-256 - 80*x + 104*x^2))*Log[2 - x]^3)/(-2*x^9 + x^10 + E^24*(-2*x^6 + x^7) + E^16*(-
6*x^7 + 3*x^8) + E^8*(-6*x^8 + 3*x^9) + (-24*x^7 - 6*x^8 + 9*x^9 + E^24*(-24*x^4 - 6*x^5 + 9*x^6) + E^16*(-72*
x^5 - 18*x^6 + 27*x^7) + E^8*(-72*x^6 - 18*x^7 + 27*x^8))*Log[2 - x] + (-96*x^5 - 96*x^6 + 18*x^7 + 27*x^8 + E
^24*(-96*x^2 - 96*x^3 + 18*x^4 + 27*x^5) + E^16*(-288*x^3 - 288*x^4 + 54*x^5 + 81*x^6) + E^8*(-288*x^4 - 288*x
^5 + 54*x^6 + 81*x^7))*Log[2 - x]^2 + (-128*x^3 - 224*x^4 - 72*x^5 + 54*x^6 + 27*x^7 + E^24*(-128 - 224*x - 72
*x^2 + 54*x^3 + 27*x^4) + E^16*(-384*x - 672*x^2 - 216*x^3 + 162*x^4 + 81*x^5) + E^8*(-384*x^2 - 672*x^3 - 216
*x^4 + 162*x^5 + 81*x^6))*Log[2 - x]^3),x]

[Out]

(16 - 13*E^8)^2/((4 - 3*E^8)^2*(E^8 + x)^2) + (8*(16 - 13*E^8))/((4 - 3*E^8)^3*(E^8 + x)) + 16/((4 - 3*E^8)^2*
(4 + 3*x)^2) - (24*(16 - 13*E^8))/((4 - 3*E^8)^3*(4 + 3*x)) - (2*(380 - 108*E^8 + 135*E^16 - 108*E^24)*Defer[I
nt][(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^(-3), x])/243 - (64*Defer[Int][1/((-2 + x)*(x^2 + 4*Log[2 - x] + 3*x
*Log[2 - x])^3), x])/(5*(2 + E^8)^2) - (2*(6 - 10*E^8 + 9*E^16)*Defer[Int][x/(x^2 + 4*Log[2 - x] + 3*x*Log[2 -
x])^3, x])/27 - (2*(5 - 6*E^8)*Defer[Int][x^2/(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3, x])/27 - (2*Defer[Int]
[x^3/(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3, x])/9 + (2*E^48*(16 - 8*E^8 + 11*E^16 - 3*E^24)*Defer[Int][1/((E
^8 + x)^2*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3), x])/((4 - 3*E^8)^3*(2 + E^8)) - (2*E^40*(768 - 416*E^8 + 6
08*E^16 - 166*E^24 - 120*E^32 + 45*E^40)*Defer[Int][1/((E^8 + x)*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3), x])
/((4 - 3*E^8)^4*(2 + E^8)^2) + (131072*Defer[Int][1/((4 + 3*x)^3*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3), x])
/(243*(4 - 3*E^8)^2) - (65536*(8 - 9*E^8)*Defer[Int][1/((4 + 3*x)^2*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^3),
x])/(243*(4 - 3*E^8)^3) + (4096*(944 - 2136*E^8 + 1341*E^16)*Defer[Int][1/((4 + 3*x)*(x^2 + 4*Log[2 - x] + 3*x
*Log[2 - x])^3), x])/(1215*(4 - 3*E^8)^4) + (2*(121 - 75*E^8)*Defer[Int][(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])
^(-2), x])/27 + (336*Defer[Int][1/((-2 + x)*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^2), x])/(5*(2 + E^8)^2) + (2
6*Defer[Int][x/(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^2, x])/9 - (2*E^48*Defer[Int][1/((E^8 + x)^3*(x^2 + 4*Log
[2 - x] + 3*x*Log[2 - x])^2), x])/(4 - 3*E^8)^2 + (2*E^24*(256 - 336*E^8 + 304*E^16 - 197*E^24 + 30*E^32)*Defe
r[Int][1/((E^8 + x)^2*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^2), x])/((4 - 3*E^8)^3*(2 + E^8)) - (4*E^16*(3072
- 4352*E^8 + 4976*E^16 - 4168*E^24 + 391*E^32 + 591*E^40 - 162*E^48)*Defer[Int][1/((E^8 + x)*(x^2 + 4*Log[2 -
x] + 3*x*Log[2 - x])^2), x])/((4 - 3*E^8)^4*(2 + E^8)^2) - (8192*Defer[Int][1/((4 + 3*x)^3*(x^2 + 4*Log[2 - x]
+ 3*x*Log[2 - x])^2), x])/(9*(4 - 3*E^8)^2) + (10240*(16 - 15*E^8)*Defer[Int][1/((4 + 3*x)^2*(x^2 + 4*Log[2 -
x] + 3*x*Log[2 - x])^2), x])/(27*(4 - 3*E^8)^3) - (256*(1008 - 2792*E^8 + 1707*E^16)*Defer[Int][1/((4 + 3*x)*
(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])^2), x])/(45*(4 - 3*E^8)^4) - (4*E^24*(16 - 13*E^8)*Defer[Int][1/((E^8 +
x)^3*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(4 - 3*E^8)^2 + (2*E^16*(192 - 304*E^8 + 117*E^16)*Defer[Int]
[1/((E^8 + x)^2*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(4 - 3*E^8)^3 + (6*E^16*(192 - 208*E^8 + 39*E^16)*
Defer[Int][1/((E^8 + x)*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(4 - 3*E^8)^4 + (512*Defer[Int][1/((4 + 3*
x)^3*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(4 - 3*E^8)^2 - (2048*(7 - 6*E^8)*Defer[Int][1/((4 + 3*x)^2*(
x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(3*(4 - 3*E^8)^3) + (64*(104 - 312*E^8 + 189*E^16)*Defer[Int][1/((4
+ 3*x)*(x^2 + 4*Log[2 - x] + 3*x*Log[2 - x])), x])/(3*(4 - 3*E^8)^4)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-4 x^5 \left (e^8+(9-4 x) x\right )-x^3 \left (x \left (400+133 x-156 x^2\right )+e^8 \left (16+21 x-4 x^2\right )\right ) \log (2-x)-x^2 \left (1536+26 \left (64+e^8\right ) x-\left (228+13 e^8\right ) x^2-494 x^3\right ) \log ^2(2-x)-\left (2048+3712 x+1376 x^2-858 x^3-507 x^4+4 e^8 \left (-32-10 x+13 x^2\right )\right ) \log ^3(2-x)\right )}{(2-x) \left (e^8+x\right )^3 \left (x^2+(4+3 x) \log (2-x)\right )^3} \, dx\\ &=2 \int \frac {-4 x^5 \left (e^8+(9-4 x) x\right )-x^3 \left (x \left (400+133 x-156 x^2\right )+e^8 \left (16+21 x-4 x^2\right )\right ) \log (2-x)-x^2 \left (1536+26 \left (64+e^8\right ) x-\left (228+13 e^8\right ) x^2-494 x^3\right ) \log ^2(2-x)-\left (2048+3712 x+1376 x^2-858 x^3-507 x^4+4 e^8 \left (-32-10 x+13 x^2\right )\right ) \log ^3(2-x)}{(2-x) \left (e^8+x\right )^3 \left (x^2+(4+3 x) \log (2-x)\right )^3} \, dx\\ &=2 \int \left (\frac {-64 \left (16-e^8\right )-4 \left (592-13 e^8\right ) x-1872 x^2-507 x^3}{\left (e^8+x\right )^3 (4+3 x)^3}-\frac {x^6 \left (16+8 x+11 x^2+3 x^3\right )}{(-2+x) \left (e^8+x\right )^2 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )^3}+\frac {x^3 \left (-256 e^8-256 \left (1+\frac {21 e^8}{16}\right ) x-336 \left (1+\frac {16 e^8}{21}\right ) x^2-264 \left (1+\frac {197 e^8}{264}\right ) x^3-199 \left (1+\frac {42 e^8}{199}\right ) x^4-39 x^5\right )}{(2-x) \left (e^8+x\right )^3 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )^2}+\frac {x^2 \left (-192 e^8-16 \left (4+13 e^8\right ) x-\left (8+39 e^8\right ) x^2+39 x^3\right )}{\left (e^8+x\right )^3 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )}\right ) \, dx\\ &=2 \int \frac {-64 \left (16-e^8\right )-4 \left (592-13 e^8\right ) x-1872 x^2-507 x^3}{\left (e^8+x\right )^3 (4+3 x)^3} \, dx-2 \int \frac {x^6 \left (16+8 x+11 x^2+3 x^3\right )}{(-2+x) \left (e^8+x\right )^2 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )^3} \, dx+2 \int \frac {x^3 \left (-256 e^8-256 \left (1+\frac {21 e^8}{16}\right ) x-336 \left (1+\frac {16 e^8}{21}\right ) x^2-264 \left (1+\frac {197 e^8}{264}\right ) x^3-199 \left (1+\frac {42 e^8}{199}\right ) x^4-39 x^5\right )}{(2-x) \left (e^8+x\right )^3 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )^2} \, dx+2 \int \frac {x^2 \left (-192 e^8-16 \left (4+13 e^8\right ) x-\left (8+39 e^8\right ) x^2+39 x^3\right )}{\left (e^8+x\right )^3 (4+3 x)^3 \left (x^2+4 \log (2-x)+3 x \log (2-x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 46, normalized size = 1.39 \begin {gather*} \frac {\left (4 x^2+(16+13 x) \log (2-x)\right )^2}{\left (e^8+x\right )^2 \left (x^2+(4+3 x) \log (2-x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8*E^8*x^5 + 72*x^6 - 32*x^7 + (800*x^4 + 266*x^5 - 312*x^6 + E^8*(32*x^3 + 42*x^4 - 8*x^5))*Log[2 -
x] + (3072*x^2 + 3328*x^3 - 456*x^4 - 988*x^5 + E^8*(52*x^3 - 26*x^4))*Log[2 - x]^2 + (4096 + 7424*x + 2752*x
^2 - 1716*x^3 - 1014*x^4 + E^8*(-256 - 80*x + 104*x^2))*Log[2 - x]^3)/(-2*x^9 + x^10 + E^24*(-2*x^6 + x^7) + E
^16*(-6*x^7 + 3*x^8) + E^8*(-6*x^8 + 3*x^9) + (-24*x^7 - 6*x^8 + 9*x^9 + E^24*(-24*x^4 - 6*x^5 + 9*x^6) + E^16
*(-72*x^5 - 18*x^6 + 27*x^7) + E^8*(-72*x^6 - 18*x^7 + 27*x^8))*Log[2 - x] + (-96*x^5 - 96*x^6 + 18*x^7 + 27*x
^8 + E^24*(-96*x^2 - 96*x^3 + 18*x^4 + 27*x^5) + E^16*(-288*x^3 - 288*x^4 + 54*x^5 + 81*x^6) + E^8*(-288*x^4 -
288*x^5 + 54*x^6 + 81*x^7))*Log[2 - x]^2 + (-128*x^3 - 224*x^4 - 72*x^5 + 54*x^6 + 27*x^7 + E^24*(-128 - 224*
x - 72*x^2 + 54*x^3 + 27*x^4) + E^16*(-384*x - 672*x^2 - 216*x^3 + 162*x^4 + 81*x^5) + E^8*(-384*x^2 - 672*x^3
- 216*x^4 + 162*x^5 + 81*x^6))*Log[2 - x]^3),x]

[Out]

(4*x^2 + (16 + 13*x)*Log[2 - x])^2/((E^8 + x)^2*(x^2 + (4 + 3*x)*Log[2 - x])^2)

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fricas [B]  time = 0.96, size = 168, normalized size = 5.09 \begin {gather*} \frac {16 \, x^{4} + {\left (169 \, x^{2} + 416 \, x + 256\right )} \log \left (-x + 2\right )^{2} + 8 \, {\left (13 \, x^{3} + 16 \, x^{2}\right )} \log \left (-x + 2\right )}{x^{6} + 2 \, x^{5} e^{8} + x^{4} e^{16} + {\left (9 \, x^{4} + 24 \, x^{3} + 16 \, x^{2} + {\left (9 \, x^{2} + 24 \, x + 16\right )} e^{16} + 2 \, {\left (9 \, x^{3} + 24 \, x^{2} + 16 \, x\right )} e^{8}\right )} \log \left (-x + 2\right )^{2} + 2 \, {\left (3 \, x^{5} + 4 \, x^{4} + {\left (3 \, x^{3} + 4 \, x^{2}\right )} e^{16} + 2 \, {\left (3 \, x^{4} + 4 \, x^{3}\right )} e^{8}\right )} \log \left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)*log(2-x)^3+((-26*x^4+52*x^3)*e
xp(4)^2-988*x^5-456*x^4+3328*x^3+3072*x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4
)*log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4)^6+(81*x^5+162*x^4-216*x^3-6
72*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)
*log(2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)*exp(4)^4+(81*x^7+54*x^6-28
8*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-
72*x^5)*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x^7-2*x^6)*exp(4)^6+(3*x^8-6*x^
7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x, algorithm="fricas")

[Out]

(16*x^4 + (169*x^2 + 416*x + 256)*log(-x + 2)^2 + 8*(13*x^3 + 16*x^2)*log(-x + 2))/(x^6 + 2*x^5*e^8 + x^4*e^16
+ (9*x^4 + 24*x^3 + 16*x^2 + (9*x^2 + 24*x + 16)*e^16 + 2*(9*x^3 + 24*x^2 + 16*x)*e^8)*log(-x + 2)^2 + 2*(3*x
^5 + 4*x^4 + (3*x^3 + 4*x^2)*e^16 + 2*(3*x^4 + 4*x^3)*e^8)*log(-x + 2))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)*log(2-x)^3+((-26*x^4+52*x^3)*e
xp(4)^2-988*x^5-456*x^4+3328*x^3+3072*x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4
)*log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4)^6+(81*x^5+162*x^4-216*x^3-6
72*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)
*log(2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)*exp(4)^4+(81*x^7+54*x^6-28
8*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-
72*x^5)*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x^7-2*x^6)*exp(4)^6+(3*x^8-6*x^
7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.16, size = 158, normalized size = 4.79

method	result	size
risch	\(\frac {169 x^{2}+416 x +256}{9 x^{2} {\mathrm e}^{16}+24 x \,{\mathrm e}^{16}+18 x^{3} {\mathrm e}^{8}+16 \,{\mathrm e}^{16}+48 x^{2} {\mathrm e}^{8}+9 x^{4}+32 x \,{\mathrm e}^{8}+24 x^{3}+16 x^{2}}-\frac {x^{3} \left (25 x^{3}+78 x^{2} \ln \left (2-x \right )+32 x^{2}+200 x \ln \left (2-x \right )+128 \ln \left (2-x \right )\right )}{\left (9 x^{2}+24 x +16\right ) \left ({\mathrm e}^{16}+2 x \,{\mathrm e}^{8}+x^{2}\right ) \left (x^{2}+3 x \ln \left (2-x \right )+4 \ln \left (2-x \right )\right )^{2}}\)	\(158\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)*ln(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2
-988*x^5-456*x^4+3328*x^3+3072*x^2)*ln(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)*ln(2-x
)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4)^6+(81*x^5+162*x^4-216*x^3-672*x^2-38
4*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*ln(2-x)^
3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)*exp(4)^4+(81*x^7+54*x^6-288*x^5-288*
x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96*x^5)*ln(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5)*exp
(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*ln(2-x)+(x^7-2*x^6)*exp(4)^6+(3*x^8-6*x^7)*exp(4)^4+
(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x,method=_RETURNVERBOSE)

[Out]

(169*x^2+416*x+256)/(9*x^2*exp(16)+24*x*exp(16)+18*x^3*exp(8)+16*exp(16)+48*x^2*exp(8)+9*x^4+32*x*exp(8)+24*x^
3+16*x^2)-x^3*(25*x^3+78*x^2*ln(2-x)+32*x^2+200*x*ln(2-x)+128*ln(2-x))/(9*x^2+24*x+16)/(exp(16)+2*x*exp(8)+x^2
)/(x^2+3*x*ln(2-x)+4*ln(2-x))^2

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maxima [B]  time = 0.73, size = 165, normalized size = 5.00 \begin {gather*} \frac {16 \, x^{4} + {\left (169 \, x^{2} + 416 \, x + 256\right )} \log \left (-x + 2\right )^{2} + 8 \, {\left (13 \, x^{3} + 16 \, x^{2}\right )} \log \left (-x + 2\right )}{x^{6} + 2 \, x^{5} e^{8} + x^{4} e^{16} + {\left (9 \, x^{4} + 6 \, x^{3} {\left (3 \, e^{8} + 4\right )} + x^{2} {\left (9 \, e^{16} + 48 \, e^{8} + 16\right )} + 8 \, x {\left (3 \, e^{16} + 4 \, e^{8}\right )} + 16 \, e^{16}\right )} \log \left (-x + 2\right )^{2} + 2 \, {\left (3 \, x^{5} + 2 \, x^{4} {\left (3 \, e^{8} + 2\right )} + x^{3} {\left (3 \, e^{16} + 8 \, e^{8}\right )} + 4 \, x^{2} e^{16}\right )} \log \left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)*log(2-x)^3+((-26*x^4+52*x^3)*e
xp(4)^2-988*x^5-456*x^4+3328*x^3+3072*x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4
)*log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4)^6+(81*x^5+162*x^4-216*x^3-6
72*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)
*log(2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)*exp(4)^4+(81*x^7+54*x^6-28
8*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-
72*x^5)*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x^7-2*x^6)*exp(4)^6+(3*x^8-6*x^
7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x, algorithm="maxima")

[Out]

(16*x^4 + (169*x^2 + 416*x + 256)*log(-x + 2)^2 + 8*(13*x^3 + 16*x^2)*log(-x + 2))/(x^6 + 2*x^5*e^8 + x^4*e^16
+ (9*x^4 + 6*x^3*(3*e^8 + 4) + x^2*(9*e^16 + 48*e^8 + 16) + 8*x*(3*e^16 + 4*e^8) + 16*e^16)*log(-x + 2)^2 + 2
*(3*x^5 + 2*x^4*(3*e^8 + 2) + x^3*(3*e^16 + 8*e^8) + 4*x^2*e^16)*log(-x + 2))

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mupad [B]  time = 4.91, size = 55, normalized size = 1.67 \begin {gather*} \frac {{\left (16\,\ln \left (2-x\right )+13\,x\,\ln \left (2-x\right )+4\,x^2\right )}^2}{{\left (x+{\mathrm {e}}^8\right )}^2\,{\left (4\,\ln \left (2-x\right )+3\,x\,\ln \left (2-x\right )+x^2\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2 - x)^2*(exp(8)*(52*x^3 - 26*x^4) + 3072*x^2 + 3328*x^3 - 456*x^4 - 988*x^5) + log(2 - x)^3*(7424*x
- exp(8)*(80*x - 104*x^2 + 256) + 2752*x^2 - 1716*x^3 - 1014*x^4 + 4096) + 8*x^5*exp(8) + log(2 - x)*(exp(8)*
(32*x^3 + 42*x^4 - 8*x^5) + 800*x^4 + 266*x^5 - 312*x^6) + 72*x^6 - 32*x^7)/(log(2 - x)*(exp(24)*(24*x^4 + 6*x
^5 - 9*x^6) + exp(8)*(72*x^6 + 18*x^7 - 27*x^8) + exp(16)*(72*x^5 + 18*x^6 - 27*x^7) + 24*x^7 + 6*x^8 - 9*x^9)
+ log(2 - x)^3*(exp(8)*(384*x^2 + 672*x^3 + 216*x^4 - 162*x^5 - 81*x^6) + exp(24)*(224*x + 72*x^2 - 54*x^3 -
27*x^4 + 128) + exp(16)*(384*x + 672*x^2 + 216*x^3 - 162*x^4 - 81*x^5) + 128*x^3 + 224*x^4 + 72*x^5 - 54*x^6 -
27*x^7) + exp(8)*(6*x^8 - 3*x^9) + exp(16)*(6*x^7 - 3*x^8) + exp(24)*(2*x^6 - x^7) + log(2 - x)^2*(96*x^5 + 9
6*x^6 - 18*x^7 - 27*x^8 + exp(24)*(96*x^2 + 96*x^3 - 18*x^4 - 27*x^5) + exp(8)*(288*x^4 + 288*x^5 - 54*x^6 - 8
1*x^7) + exp(16)*(288*x^3 + 288*x^4 - 54*x^5 - 81*x^6)) + 2*x^9 - x^10),x)

[Out]

(16*log(2 - x) + 13*x*log(2 - x) + 4*x^2)^2/((x + exp(8))^2*(4*log(2 - x) + 3*x*log(2 - x) + x^2)^2)

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sympy [B]  time = 2.34, size = 360, normalized size = 10.91 \begin {gather*} - \frac {- 169 x^{2} - 416 x - 256}{9 x^{4} + x^{3} \left (24 + 18 e^{8}\right ) + x^{2} \left (16 + 48 e^{8} + 9 e^{16}\right ) + x \left (32 e^{8} + 24 e^{16}\right ) + 16 e^{16}} + \frac {- 25 x^{6} - 32 x^{5} + \left (- 78 x^{5} - 200 x^{4} - 128 x^{3}\right ) \log {\left (2 - x \right )}}{9 x^{8} + 24 x^{7} + 18 x^{7} e^{8} + 16 x^{6} + 48 x^{6} e^{8} + 9 x^{6} e^{16} + 32 x^{5} e^{8} + 24 x^{5} e^{16} + 16 x^{4} e^{16} + \left (54 x^{7} + 216 x^{6} + 108 x^{6} e^{8} + 288 x^{5} + 432 x^{5} e^{8} + 54 x^{5} e^{16} + 128 x^{4} + 576 x^{4} e^{8} + 216 x^{4} e^{16} + 256 x^{3} e^{8} + 288 x^{3} e^{16} + 128 x^{2} e^{16}\right ) \log {\left (2 - x \right )} + \left (81 x^{6} + 432 x^{5} + 162 x^{5} e^{8} + 864 x^{4} + 864 x^{4} e^{8} + 81 x^{4} e^{16} + 768 x^{3} + 1728 x^{3} e^{8} + 432 x^{3} e^{16} + 256 x^{2} + 1536 x^{2} e^{8} + 864 x^{2} e^{16} + 512 x e^{8} + 768 x e^{16} + 256 e^{16}\right ) \log {\left (2 - x \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((104*x**2-80*x-256)*exp(4)**2-1014*x**4-1716*x**3+2752*x**2+7424*x+4096)*ln(2-x)**3+((-26*x**4+52*
x**3)*exp(4)**2-988*x**5-456*x**4+3328*x**3+3072*x**2)*ln(2-x)**2+((-8*x**5+42*x**4+32*x**3)*exp(4)**2-312*x**
6+266*x**5+800*x**4)*ln(2-x)+8*x**5*exp(4)**2-32*x**7+72*x**6)/(((27*x**4+54*x**3-72*x**2-224*x-128)*exp(4)**6
+(81*x**5+162*x**4-216*x**3-672*x**2-384*x)*exp(4)**4+(81*x**6+162*x**5-216*x**4-672*x**3-384*x**2)*exp(4)**2+
27*x**7+54*x**6-72*x**5-224*x**4-128*x**3)*ln(2-x)**3+((27*x**5+18*x**4-96*x**3-96*x**2)*exp(4)**6+(81*x**6+54
*x**5-288*x**4-288*x**3)*exp(4)**4+(81*x**7+54*x**6-288*x**5-288*x**4)*exp(4)**2+27*x**8+18*x**7-96*x**6-96*x*
*5)*ln(2-x)**2+((9*x**6-6*x**5-24*x**4)*exp(4)**6+(27*x**7-18*x**6-72*x**5)*exp(4)**4+(27*x**8-18*x**7-72*x**6
)*exp(4)**2+9*x**9-6*x**8-24*x**7)*ln(2-x)+(x**7-2*x**6)*exp(4)**6+(3*x**8-6*x**7)*exp(4)**4+(3*x**9-6*x**8)*e
xp(4)**2+x**10-2*x**9),x)

[Out]

-(-169*x**2 - 416*x - 256)/(9*x**4 + x**3*(24 + 18*exp(8)) + x**2*(16 + 48*exp(8) + 9*exp(16)) + x*(32*exp(8)
+ 24*exp(16)) + 16*exp(16)) + (-25*x**6 - 32*x**5 + (-78*x**5 - 200*x**4 - 128*x**3)*log(2 - x))/(9*x**8 + 24*
x**7 + 18*x**7*exp(8) + 16*x**6 + 48*x**6*exp(8) + 9*x**6*exp(16) + 32*x**5*exp(8) + 24*x**5*exp(16) + 16*x**4
*exp(16) + (54*x**7 + 216*x**6 + 108*x**6*exp(8) + 288*x**5 + 432*x**5*exp(8) + 54*x**5*exp(16) + 128*x**4 + 5
76*x**4*exp(8) + 216*x**4*exp(16) + 256*x**3*exp(8) + 288*x**3*exp(16) + 128*x**2*exp(16))*log(2 - x) + (81*x*
*6 + 432*x**5 + 162*x**5*exp(8) + 864*x**4 + 864*x**4*exp(8) + 81*x**4*exp(16) + 768*x**3 + 1728*x**3*exp(8) +
432*x**3*exp(16) + 256*x**2 + 1536*x**2*exp(8) + 864*x**2*exp(16) + 512*x*exp(8) + 768*x*exp(16) + 256*exp(16
))*log(2 - x)**2)

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