3.14.50 \(\int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} (-120 x^4-96 x^5-18 x^6+24 x^7)+(-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}) \log (2)+(-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}) \log ^2(2)+(-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}) \log ^3(2)+(-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}) \log ^4(2)+e^{3 x} (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+(1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8) \log (2))+e^{2 x} (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+(-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9) \log (2)+(-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9) \log ^2(2))+e^x (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+(518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}) \log (2)+(138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}) \log ^2(2)+(12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}) \log ^3(2))}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx\)
Optimal. Leaf size=27 \[ 6 x \left (-4-\frac {1+e^x x}{-4+x^2}-\log (2)\right )^4 \]
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Rubi [B] time = 6.02, antiderivative size = 1088, normalized size of antiderivative = 40.30,
number of steps used = 39, number of rules used = 8, integrand size = 609, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used
= {6688, 12, 6742, 2288, 288, 321, 207, 199}
result too large to display
Antiderivative was successfully verified.
[In]
Int[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 + E^(4*x)*(-120*x^4 - 96*x^5 - 1
8*x^6 + 24*x^7) + (-1296000 + 1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-518400
+ 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^2 + (-92160 + 119808*x^2 - 61440*x^4 + 1
5552*x^6 - 1944*x^8 + 96*x^10)*Log[2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log[2]^4
+ E^(3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (1536*x^3 + 1152*x^4 - 192*x^5 - 576
*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^(2*x)*(-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 13248*x
^7 - 576*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368*x^6 - 6768*x^7 - 288*x^8 + 57
6*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880*x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2]^2) +
E^x*(648000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8 + 1536
*x^10 + (518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1
152*x^10)*Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4536*x^
8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 +
24*x^10)*Log[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]
[Out]
(6*E^(4*x)*x^4*(4*x - x^3))/(4 - x^2)^5 + (945*x*(4 + Log[2])^4)/64 - (3*x^9*(4 + Log[2])^4)/(4*(4 - x^2)^4) +
(9*x^7*(4 + Log[2])^4)/(8*(4 - x^2)^3) - (63*x^5*(4 + Log[2])^4)/(32*(4 - x^2)^2) + (315*x^3*(4 + Log[2])^4)/
(64*(4 - x^2)) - (945*ArcTanh[x/2]*(4 + Log[2])^4)/32 + (3*x*(15 + Log[16])^4)/(4*(4 - x^2)^4) + (7*x*(15 + Lo
g[16])^4)/(32*(4 - x^2)^3) + (35*x*(15 + Log[16])^4)/(512*(4 - x^2)^2) + (105*x*(15 + Log[16])^4)/(4096*(4 - x
^2)) + (105*ArcTanh[x/2]*(15 + Log[16])^4)/8192 - (24*E^(3*x)*x^3*(x^5*(4 + Log[2]) + 4*x*(15 + Log[16]) - x^3
*(31 + Log[256])))/(4 - x^2)^5 + (36*E^(2*x)*x^2*(15 - x^2*(4 + Log[2]) + Log[16])*(x^5*(4 + Log[2]) + 4*x*(15
+ Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 - (24*E^x*x*(15 - x^2*(4 + Log[2]) + Log[16])^2*(x^5*(4 + Log[
2]) + 4*x*(15 + Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 + (3*x^3*(4 + Log[2])*(15 + Log[16])^2*(180 + Log
[16] + 3*Log[256] + Log[4096]))/(4*(4 - x^2)^4) - (3*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[25
6] + Log[4096]))/(8*(4 - x^2)^3) + (3*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096])
)/(128*(4 - x^2)^2) + (9*x*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/(1024*(4 -
x^2)) + (9*ArcTanh[x/2]*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/2048 - (3*x^5*
(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(4 - x^2)^4 + (5*x^3*(4 + Log[2])^3*(
15 + Log[16])*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(2*(4 - x^2)^3) - (15*x*(4 + Log[2])^3*(15 + Log[16])
*(1 + (3*(54 + Log[4096]))/(16 + Log[16])))/(8*(4 - x^2)^2) + (15*x*(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54
+ Log[4096]))/(16 + Log[16])))/(64*(4 - x^2)) + (15*ArcTanh[x/2]*(4 + Log[2])^3*(15 + Log[16])*(1 + (3*(54 + L
og[4096]))/(16 + Log[16])))/128 + (9*x^7*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(4*(4 - x^2)^4*(45
+ Log[4096])) - (21*x^5*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(8*(4 - x^2)^3*(45 + Log[4096])) +
(105*x^3*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(32*(4 - x^2)^2*(45 + Log[4096])) - (315*x*(4 + L
og[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(64*(4 - x^2)*(45 + Log[4096])) + (315*ArcTanh[x/2]*(4 + Log[2])^
3*(15 + Log[16])*(84 + Log[1048576]))/(128*(45 + Log[4096])) - (9*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[10
48576]))/((4 - x^2)^4*(48 + Log[4096])) + (3*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(8*(4 - x^2)
^3*(48 + Log[4096])) + (15*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(128*(4 - x^2)^2*(48 + Log[409
6])) + (45*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(1024*(4 - x^2)*(48 + Log[4096])) + (45*ArcTan
h[x/2]*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(2048*(48 + Log[4096]))
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 199
Int[((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> -Simp[(x*(a + b*x^n)^(p + 1))/(a*n*(p + 1)), x] + Dist[(n*(p +
1) + 1)/(a*n*(p + 1)), Int[(a + b*x^n)^(p + 1), x], x] /; FreeQ[{a, b}, x] && IGtQ[n, 0] && LtQ[p, -1] && (In
tegerQ[2*p] || (n == 2 && IntegerQ[4*p]) || (n == 2 && IntegerQ[3*p]) || Denominator[p + 1/n] < Denominator[p]
)
Rule 207
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTanh[(Rt[b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[b, 2]), x] /;
FreeQ[{a, b}, x] && NegQ[a/b] && (LtQ[a, 0] || GtQ[b, 0])
Rule 288
Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c^(n - 1)*(c*x)^(m - n + 1)*(a + b*x^
n)^(p + 1))/(b*n*(p + 1)), x] - Dist[(c^n*(m - n + 1))/(b*n*(p + 1)), Int[(c*x)^(m - n)*(a + b*x^n)^(p + 1), x
], x] /; FreeQ[{a, b, c}, x] && IGtQ[n, 0] && LtQ[p, -1] && GtQ[m + 1, n] && !ILtQ[(m + n*(p + 1) + 1)/n, 0]
&& IntBinomialQ[a, b, c, n, m, p, x]
Rule 321
Int[((c_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(c^(n - 1)*(c*x)^(m - n + 1)*(a + b*x^n
)^(p + 1))/(b*(m + n*p + 1)), x] - Dist[(a*c^n*(m - n + 1))/(b*(m + n*p + 1)), Int[(c*x)^(m - n)*(a + b*x^n)^p
, x], x] /; FreeQ[{a, b, c, p}, x] && IGtQ[n, 0] && GtQ[m, n - 1] && NeQ[m + n*p + 1, 0] && IntBinomialQ[a, b,
c, n, m, p, x]
Rule 2288
Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]
Rule 6688
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rule 6742
Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 \left (e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )+x^2 (4+\log (2))\right )^3 \left (-e^x x \left (-20-16 x-3 x^2+4 x^3\right )-60 \left (1+\frac {4 \log (2)}{15}\right )-x^4 (4+\log (2))+x^2 (39+\log (256))\right )}{\left (4-x^2\right )^5} \, dx\\ &=6 \int \frac {\left (e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )+x^2 (4+\log (2))\right )^3 \left (-e^x x \left (-20-16 x-3 x^2+4 x^3\right )-60 \left (1+\frac {4 \log (2)}{15}\right )-x^4 (4+\log (2))+x^2 (39+\log (256))\right )}{\left (4-x^2\right )^5} \, dx\\ &=6 \int \left (\frac {e^{4 x} x^4 \left (-20-16 x-3 x^2+4 x^3\right )}{\left (-4+x^2\right )^5}+\frac {e^{3 x} x^3 \left (144 x^2 \left (1+\frac {2 \log (2)}{9}\right )+32 x^4 \left (1+\frac {\log (2)}{4}\right )-48 x^5 \left (1+\frac {\log (2)}{4}\right )+372 x^3 \left (1+\frac {8 \log (2)}{31}\right )-960 \left (1+\frac {4 \log (2)}{15}\right )-720 x \left (1+\frac {4 \log (2)}{15}\right )\right )}{\left (4-x^2\right )^5}+\frac {x^{10} (4+\log (2))^4}{\left (-4+x^2\right )^5}+\frac {3 e^{2 x} x^2 \left (74 x^2 \left (1+\frac {8 \log (2)}{37}\right )+8 x^4 \left (1+\frac {\log (2)}{4}\right )-16 x^5 \left (1+\frac {\log (2)}{4}\right )+124 x^3 \left (1+\frac {8 \log (2)}{31}\right )-360 \left (1+\frac {4 \log (2)}{15}\right )-240 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (4-x^2\right )^5}-\frac {4 (15+\log (16))^4}{\left (-4+x^2\right )^5}+\frac {4 e^x x \left (38 x^2 \left (1+\frac {4 \log (2)}{19}\right )-4 x^5 \left (1+\frac {\log (2)}{4}\right )+31 x^3 \left (1+\frac {8 \log (2)}{31}\right )-120 \left (1+\frac {4 \log (2)}{15}\right )-60 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (15-x^2 (4+\log (2))+\log (16)\right )^2}{\left (4-x^2\right )^5}-\frac {12 x^4 (4+\log (2))^2 (15+\log (16))^2 \left (1+\frac {\log (16)+3 (44+\log (256))}{12 (4+\log (2))}\right )}{\left (-4+x^2\right )^5}-\frac {3 x^8 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )}{\left (-4+x^2\right )^5}+\frac {12 x^2 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )}{\left (-4+x^2\right )^5}+\frac {4 x^6 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (-4+x^2\right )^5}\right ) \, dx\\ &=6 \int \frac {e^{4 x} x^4 \left (-20-16 x-3 x^2+4 x^3\right )}{\left (-4+x^2\right )^5} \, dx+6 \int \frac {e^{3 x} x^3 \left (144 x^2 \left (1+\frac {2 \log (2)}{9}\right )+32 x^4 \left (1+\frac {\log (2)}{4}\right )-48 x^5 \left (1+\frac {\log (2)}{4}\right )+372 x^3 \left (1+\frac {8 \log (2)}{31}\right )-960 \left (1+\frac {4 \log (2)}{15}\right )-720 x \left (1+\frac {4 \log (2)}{15}\right )\right )}{\left (4-x^2\right )^5} \, dx+18 \int \frac {e^{2 x} x^2 \left (74 x^2 \left (1+\frac {8 \log (2)}{37}\right )+8 x^4 \left (1+\frac {\log (2)}{4}\right )-16 x^5 \left (1+\frac {\log (2)}{4}\right )+124 x^3 \left (1+\frac {8 \log (2)}{31}\right )-360 \left (1+\frac {4 \log (2)}{15}\right )-240 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (4-x^2\right )^5} \, dx+24 \int \frac {e^x x \left (38 x^2 \left (1+\frac {4 \log (2)}{19}\right )-4 x^5 \left (1+\frac {\log (2)}{4}\right )+31 x^3 \left (1+\frac {8 \log (2)}{31}\right )-120 \left (1+\frac {4 \log (2)}{15}\right )-60 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (15-x^2 (4+\log (2))+\log (16)\right )^2}{\left (4-x^2\right )^5} \, dx+\left (6 (4+\log (2))^4\right ) \int \frac {x^{10}}{\left (-4+x^2\right )^5} \, dx-\left (24 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^5} \, dx-\left (6 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {x^4}{\left (-4+x^2\right )^5} \, dx-\left (18 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^8}{\left (-4+x^2\right )^5} \, dx+\left (72 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {x^2}{\left (-4+x^2\right )^5} \, dx+\left (24 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {x^6}{\left (-4+x^2\right )^5} \, dx\\ &=\frac {6 e^{4 x} x^4 \left (4 x-x^3\right )}{\left (4-x^2\right )^5}-\frac {3 x^9 (4+\log (2))^4}{4 \left (4-x^2\right )^4}+\frac {3 x (15+\log (16))^4}{4 \left (4-x^2\right )^4}-\frac {24 e^{3 x} x^3 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {36 e^{2 x} x^2 \left (15-x^2 (4+\log (2))+\log (16)\right ) \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}-\frac {24 e^x x \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {9 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{4 \left (4-x^2\right )^4 (45+\log (4096))}-\frac {9 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{\left (4-x^2\right )^4 (48+\log (4096))}+\frac {3 x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{4 \left (4-x^2\right )^4}-\frac {3 x^5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (4-x^2\right )^4}+\frac {1}{4} \left (27 (4+\log (2))^4\right ) \int \frac {x^8}{\left (-4+x^2\right )^4} \, dx+\frac {1}{4} \left (21 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^4} \, dx-\frac {1}{4} \left (9 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {x^2}{\left (-4+x^2\right )^4} \, dx-\frac {1}{4} \left (63 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^6}{\left (-4+x^2\right )^4} \, dx+\left (9 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {1}{\left (-4+x^2\right )^4} \, dx+\left (15 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {x^4}{\left (-4+x^2\right )^4} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 4.68, size = 699, normalized size = 25.89 \begin {gather*} 6 \left (\frac {e^{4 x} x^5}{\left (-4+x^2\right )^4}+\frac {x^9 (4+\log (2))^4}{\left (-4+x^2\right )^4}-\frac {3 \left (2 x \left (-6720+6160 x^2-2044 x^4+279 x^6\right )+105 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^4}{64 \left (-4+x^2\right )^4}+\frac {4 e^{3 x} x^4 \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (-4+x^2\right )^4}+\frac {x (15+\log (16))^4}{8 \left (-4+x^2\right )^4}+\frac {7 \left (-2 x \left (528-160 x^2+15 x^4\right )+15 \left (-4+x^2\right )^3 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (15+\log (16))^4}{49152 \left (-4+x^2\right )^3}+\frac {6 e^{2 x} x^3 \left (-15-4 \log (2)+x^2 (4+\log (2))\right ) \left (x^4 (4+\log (2))+4 (15+\log (16))-x^2 (31+\log (256))\right )}{\left (-4+x^2\right )^5}+\frac {4 e^x x^2 \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^4 (4+\log (2))+4 (15+\log (16))-x^2 (31+\log (256))\right )}{\left (-4+x^2\right )^5}+\frac {x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{5 \left (-4+x^2\right )^4}+\frac {\left (-2 x \left (960+1168 x^2-220 x^4+15 x^6\right )+15 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{20480 \left (-4+x^2\right )^4}-\frac {4 x^5 (4+\log (2))^3 (15+\log (16)) (178+\log (16)+3 \log (4096))}{3 \left (-4+x^2\right )^4 (16+\log (16))}+\frac {5 \left (-384 x+352 x^3+88 x^5-6 x^7+3 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^3 (15+\log (16)) (178+\log (16)+3 \log (4096))}{768 \left (-4+x^2\right )^4 (16+\log (16))}+\frac {3 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (1048576))}{\left (-4+x^2\right )^4 (45+\log (4096))}+\frac {7 \left (-2 x \left (960-880 x^2+292 x^4+15 x^6\right )+15 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^3 (15+\log (16)) (84+\log (1048576))}{256 \left (-4+x^2\right )^4 (45+\log (4096))}-\frac {12 x (4+\log (2)) (15+\log (16))^3 (87+\log (1048576))}{7 \left (-4+x^2\right )^4 (48+\log (4096))}+\frac {\left (35712 x-16352 x^3+3080 x^5-210 x^7+105 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2)) (15+\log (16))^3 (87+\log (1048576))}{28672 \left (-4+x^2\right )^4 (48+\log (4096))}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 + E^(4*x)*(-120*x^4 - 96*x
^5 - 18*x^6 + 24*x^7) + (-1296000 + 1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-
518400 + 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^2 + (-92160 + 119808*x^2 - 61440*x
^4 + 15552*x^6 - 1944*x^8 + 96*x^10)*Log[2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log
[2]^4 + E^(3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (1536*x^3 + 1152*x^4 - 192*x^5
- 576*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^(2*x)*(-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 1
3248*x^7 - 576*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368*x^6 - 6768*x^7 - 288*x^
8 + 576*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880*x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2
]^2) + E^x*(648000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8
+ 1536*x^10 + (518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x
^8 + 1152*x^10)*Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4
536*x^8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384
*x^8 + 24*x^10)*Log[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]
[Out]
6*((E^(4*x)*x^5)/(-4 + x^2)^4 + (x^9*(4 + Log[2])^4)/(-4 + x^2)^4 - (3*(2*x*(-6720 + 6160*x^2 - 2044*x^4 + 279
*x^6) + 105*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^4)/(64*(-4 + x^2)^4) + (4*E^(3*x)*x^4*(-15 - 4*Log[2] + x^
2*(4 + Log[2])))/(-4 + x^2)^4 + (x*(15 + Log[16])^4)/(8*(-4 + x^2)^4) + (7*(-2*x*(528 - 160*x^2 + 15*x^4) + 15
*(-4 + x^2)^3*ArcTanh[x/2])*(15 + Log[16])^4)/(49152*(-4 + x^2)^3) + (6*E^(2*x)*x^3*(-15 - 4*Log[2] + x^2*(4 +
Log[2]))*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*(31 + Log[256])))/(-4 + x^2)^5 + (4*E^x*x^2*(15 - x^2*(4
+ Log[2]) + Log[16])^2*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*(31 + Log[256])))/(-4 + x^2)^5 + (x^3*(4 + L
og[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] + Log[4096]))/(5*(-4 + x^2)^4) + ((-2*x*(960 + 1168*x^2 -
220*x^4 + 15*x^6) + 15*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])*(15 + Log[16])^2*(180 + Log[16] + 3*Log[256] +
Log[4096]))/(20480*(-4 + x^2)^4) - (4*x^5*(4 + Log[2])^3*(15 + Log[16])*(178 + Log[16] + 3*Log[4096]))/(3*(-4
+ x^2)^4*(16 + Log[16])) + (5*(-384*x + 352*x^3 + 88*x^5 - 6*x^7 + 3*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^3
*(15 + Log[16])*(178 + Log[16] + 3*Log[4096]))/(768*(-4 + x^2)^4*(16 + Log[16])) + (3*x^7*(4 + Log[2])^3*(15 +
Log[16])*(84 + Log[1048576]))/((-4 + x^2)^4*(45 + Log[4096])) + (7*(-2*x*(960 - 880*x^2 + 292*x^4 + 15*x^6) +
15*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[1048576]))/(256*(-4 + x^2)^4*(45 + Log[
4096])) - (12*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1048576]))/(7*(-4 + x^2)^4*(48 + Log[4096])) + ((35712
*x - 16352*x^3 + 3080*x^5 - 210*x^7 + 105*(-4 + x^2)^4*ArcTanh[x/2])*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[1
048576]))/(28672*(-4 + x^2)^4*(48 + Log[4096])))
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fricas [B] time = 0.88, size = 362, normalized size = 13.41 \begin {gather*} \frac {6 \, {\left (256 \, x^{9} - 3840 \, x^{7} + x^{5} e^{\left (4 \, x\right )} + 21600 \, x^{5} + {\left (x^{9} - 16 \, x^{7} + 96 \, x^{5} - 256 \, x^{3} + 256 \, x\right )} \log \relax (2)^{4} + 4 \, {\left (4 \, x^{9} - 63 \, x^{7} + 372 \, x^{5} - 976 \, x^{3} + 960 \, x\right )} \log \relax (2)^{3} - 54000 \, x^{3} + 6 \, {\left (16 \, x^{9} - 248 \, x^{7} + 1441 \, x^{5} - 3720 \, x^{3} + 3600 \, x\right )} \log \relax (2)^{2} + 4 \, {\left (4 \, x^{6} - 15 \, x^{4} + {\left (x^{6} - 4 \, x^{4}\right )} \log \relax (2)\right )} e^{\left (3 \, x\right )} + 6 \, {\left (16 \, x^{7} - 120 \, x^{5} + 225 \, x^{3} + {\left (x^{7} - 8 \, x^{5} + 16 \, x^{3}\right )} \log \relax (2)^{2} + 2 \, {\left (4 \, x^{7} - 31 \, x^{5} + 60 \, x^{3}\right )} \log \relax (2)\right )} e^{\left (2 \, x\right )} + 4 \, {\left (64 \, x^{8} - 720 \, x^{6} + 2700 \, x^{4} + {\left (x^{8} - 12 \, x^{6} + 48 \, x^{4} - 64 \, x^{2}\right )} \log \relax (2)^{3} + 3 \, {\left (4 \, x^{8} - 47 \, x^{6} + 184 \, x^{4} - 240 \, x^{2}\right )} \log \relax (2)^{2} - 3375 \, x^{2} + 3 \, {\left (16 \, x^{8} - 184 \, x^{6} + 705 \, x^{4} - 900 \, x^{2}\right )} \log \relax (2)\right )} e^{x} + 4 \, {\left (64 \, x^{9} - 976 \, x^{7} + 5580 \, x^{5} - 14175 \, x^{3} + 13500 \, x\right )} \log \relax (2) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="fricas")
[Out]
6*(256*x^9 - 3840*x^7 + x^5*e^(4*x) + 21600*x^5 + (x^9 - 16*x^7 + 96*x^5 - 256*x^3 + 256*x)*log(2)^4 + 4*(4*x^
9 - 63*x^7 + 372*x^5 - 976*x^3 + 960*x)*log(2)^3 - 54000*x^3 + 6*(16*x^9 - 248*x^7 + 1441*x^5 - 3720*x^3 + 360
0*x)*log(2)^2 + 4*(4*x^6 - 15*x^4 + (x^6 - 4*x^4)*log(2))*e^(3*x) + 6*(16*x^7 - 120*x^5 + 225*x^3 + (x^7 - 8*x
^5 + 16*x^3)*log(2)^2 + 2*(4*x^7 - 31*x^5 + 60*x^3)*log(2))*e^(2*x) + 4*(64*x^8 - 720*x^6 + 2700*x^4 + (x^8 -
12*x^6 + 48*x^4 - 64*x^2)*log(2)^3 + 3*(4*x^8 - 47*x^6 + 184*x^4 - 240*x^2)*log(2)^2 - 3375*x^2 + 3*(16*x^8 -
184*x^6 + 705*x^4 - 900*x^2)*log(2))*e^x + 4*(64*x^9 - 976*x^7 + 5580*x^5 - 14175*x^3 + 13500*x)*log(2) + 5062
5*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)
________________________________________________________________________________________
giac [B] time = 0.63, size = 508, normalized size = 18.81 \begin {gather*} \frac {6 \, {\left (x^{9} \log \relax (2)^{4} + 16 \, x^{9} \log \relax (2)^{3} + 4 \, x^{8} e^{x} \log \relax (2)^{3} + 96 \, x^{9} \log \relax (2)^{2} + 48 \, x^{8} e^{x} \log \relax (2)^{2} - 16 \, x^{7} \log \relax (2)^{4} + 256 \, x^{9} \log \relax (2) + 192 \, x^{8} e^{x} \log \relax (2) + 6 \, x^{7} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 252 \, x^{7} \log \relax (2)^{3} - 48 \, x^{6} e^{x} \log \relax (2)^{3} + 256 \, x^{9} + 256 \, x^{8} e^{x} + 48 \, x^{7} e^{\left (2 \, x\right )} \log \relax (2) - 1488 \, x^{7} \log \relax (2)^{2} - 564 \, x^{6} e^{x} \log \relax (2)^{2} + 96 \, x^{5} \log \relax (2)^{4} + 96 \, x^{7} e^{\left (2 \, x\right )} - 3904 \, x^{7} \log \relax (2) + 4 \, x^{6} e^{\left (3 \, x\right )} \log \relax (2) - 2208 \, x^{6} e^{x} \log \relax (2) - 48 \, x^{5} e^{\left (2 \, x\right )} \log \relax (2)^{2} + 1488 \, x^{5} \log \relax (2)^{3} + 192 \, x^{4} e^{x} \log \relax (2)^{3} - 3840 \, x^{7} + 16 \, x^{6} e^{\left (3 \, x\right )} - 2880 \, x^{6} e^{x} - 372 \, x^{5} e^{\left (2 \, x\right )} \log \relax (2) + 8646 \, x^{5} \log \relax (2)^{2} + 2208 \, x^{4} e^{x} \log \relax (2)^{2} - 256 \, x^{3} \log \relax (2)^{4} + x^{5} e^{\left (4 \, x\right )} - 720 \, x^{5} e^{\left (2 \, x\right )} + 22320 \, x^{5} \log \relax (2) - 16 \, x^{4} e^{\left (3 \, x\right )} \log \relax (2) + 8460 \, x^{4} e^{x} \log \relax (2) + 96 \, x^{3} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 3904 \, x^{3} \log \relax (2)^{3} - 256 \, x^{2} e^{x} \log \relax (2)^{3} + 21600 \, x^{5} - 60 \, x^{4} e^{\left (3 \, x\right )} + 10800 \, x^{4} e^{x} + 720 \, x^{3} e^{\left (2 \, x\right )} \log \relax (2) - 22320 \, x^{3} \log \relax (2)^{2} - 2880 \, x^{2} e^{x} \log \relax (2)^{2} + 256 \, x \log \relax (2)^{4} + 1350 \, x^{3} e^{\left (2 \, x\right )} - 56700 \, x^{3} \log \relax (2) - 10800 \, x^{2} e^{x} \log \relax (2) + 3840 \, x \log \relax (2)^{3} - 54000 \, x^{3} - 13500 \, x^{2} e^{x} + 21600 \, x \log \relax (2)^{2} + 54000 \, x \log \relax (2) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="giac")
[Out]
6*(x^9*log(2)^4 + 16*x^9*log(2)^3 + 4*x^8*e^x*log(2)^3 + 96*x^9*log(2)^2 + 48*x^8*e^x*log(2)^2 - 16*x^7*log(2)
^4 + 256*x^9*log(2) + 192*x^8*e^x*log(2) + 6*x^7*e^(2*x)*log(2)^2 - 252*x^7*log(2)^3 - 48*x^6*e^x*log(2)^3 + 2
56*x^9 + 256*x^8*e^x + 48*x^7*e^(2*x)*log(2) - 1488*x^7*log(2)^2 - 564*x^6*e^x*log(2)^2 + 96*x^5*log(2)^4 + 96
*x^7*e^(2*x) - 3904*x^7*log(2) + 4*x^6*e^(3*x)*log(2) - 2208*x^6*e^x*log(2) - 48*x^5*e^(2*x)*log(2)^2 + 1488*x
^5*log(2)^3 + 192*x^4*e^x*log(2)^3 - 3840*x^7 + 16*x^6*e^(3*x) - 2880*x^6*e^x - 372*x^5*e^(2*x)*log(2) + 8646*
x^5*log(2)^2 + 2208*x^4*e^x*log(2)^2 - 256*x^3*log(2)^4 + x^5*e^(4*x) - 720*x^5*e^(2*x) + 22320*x^5*log(2) - 1
6*x^4*e^(3*x)*log(2) + 8460*x^4*e^x*log(2) + 96*x^3*e^(2*x)*log(2)^2 - 3904*x^3*log(2)^3 - 256*x^2*e^x*log(2)^
3 + 21600*x^5 - 60*x^4*e^(3*x) + 10800*x^4*e^x + 720*x^3*e^(2*x)*log(2) - 22320*x^3*log(2)^2 - 2880*x^2*e^x*lo
g(2)^2 + 256*x*log(2)^4 + 1350*x^3*e^(2*x) - 56700*x^3*log(2) - 10800*x^2*e^x*log(2) + 3840*x*log(2)^3 - 54000
*x^3 - 13500*x^2*e^x + 21600*x*log(2)^2 + 54000*x*log(2) + 50625*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)
________________________________________________________________________________________
maple [B] time = 0.33, size = 380, normalized size = 14.07
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\(6 x \ln \relax (2)^{4}+96 x \ln \relax (2)^{3}+576 x \ln \relax (2)^{2}+1536 x \ln \relax (2)+1536 x +\frac {\left (24 \ln \relax (2)^{3}+288 \ln \relax (2)^{2}+1152 \ln \relax (2)+1536\right ) x^{7}+\left (-288 \ln \relax (2)^{3}-3420 \ln \relax (2)^{2}-13536 \ln \relax (2)-17856\right ) x^{5}+\left (1152 \ln \relax (2)^{3}+13536 \ln \relax (2)^{2}+53016 \ln \relax (2)+69216\right ) x^{3}+\left (-1536 \ln \relax (2)^{3}-17856 \ln \relax (2)^{2}-69216 \ln \relax (2)-89466\right ) x}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}+\frac {6 x^{5} {\mathrm e}^{4 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{4} \left (x^{2} \ln \relax (2)+4 x^{2}-4 \ln \relax (2)-15\right ) {\mathrm e}^{3 x}}{\left (x^{2}-4\right )^{4}}+\frac {36 x^{3} \left (x^{4} \ln \relax (2)^{2}+8 x^{4} \ln \relax (2)-8 x^{2} \ln \relax (2)^{2}+16 x^{4}-62 x^{2} \ln \relax (2)+16 \ln \relax (2)^{2}-120 x^{2}+120 \ln \relax (2)+225\right ) {\mathrm e}^{2 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{2} \left (x^{6} \ln \relax (2)^{3}+12 x^{6} \ln \relax (2)^{2}-12 x^{4} \ln \relax (2)^{3}+48 x^{6} \ln \relax (2)-141 x^{4} \ln \relax (2)^{2}+64 x^{6}+48 x^{2} \ln \relax (2)^{3}-552 x^{4} \ln \relax (2)+552 x^{2} \ln \relax (2)^{2}-720 x^{4}-64 \ln \relax (2)^{3}+2115 x^{2} \ln \relax (2)-720 \ln \relax (2)^{2}+2700 x^{2}-2700 \ln \relax (2)-3375\right ) {\mathrm e}^{x}}{\left (x^{2}-4\right )^{4}}\) |
\(380\) |
default |
\(1536 x -\frac {9 \ln \relax (2)^{2}}{2 \left (2+x \right )^{2}}+1536 \,{\mathrm e}^{x}+24 \ln \relax (2)^{3} {\mathrm e}^{x}+288 \ln \relax (2)^{2} {\mathrm e}^{x}+96 x \ln \relax (2)^{3}+\frac {3}{64 \left (x -2\right )^{4}}+1152 \,{\mathrm e}^{x} \ln \relax (2)+\frac {768}{2+x}+6 x \ln \relax (2)^{4}+576 x \ln \relax (2)^{2}+1536 x \ln \relax (2)+\frac {768}{x -2}+\frac {3 \,{\mathrm e}^{x}}{8 \left (2+x \right )^{4}}+\frac {18717 \,{\mathrm e}^{x}}{64 \left (2+x \right )^{2}}-\frac {18 \,{\mathrm e}^{x}}{\left (2+x \right )^{3}}-\frac {214755 \,{\mathrm e}^{x}}{128 \left (2+x \right )}+\frac {18 \,{\mathrm e}^{x}}{\left (x -2\right )^{3}}+\frac {214755 \,{\mathrm e}^{x}}{128 \left (x -2\right )}+\frac {18717 \,{\mathrm e}^{x}}{64 \left (x -2\right )^{2}}+\frac {3 \,{\mathrm e}^{x}}{8 \left (x -2\right )^{4}}+\frac {12 \ln \relax (2)^{3}}{x -2}+\frac {12 \ln \relax (2)^{3}}{2+x}+\frac {144 \ln \relax (2)^{2}}{2+x}+\frac {9 \ln \relax (2)^{2}}{2 \left (x -2\right )^{2}}+\frac {144 \ln \relax (2)^{2}}{x -2}+\frac {3 \ln \relax (2)}{4 \left (x -2\right )^{3}}+\frac {573 \ln \relax (2)}{16 \left (x -2\right )^{2}}+\frac {576 \ln \relax (2)}{x -2}+\frac {3 \ln \relax (2)}{4 \left (2+x \right )^{3}}-\frac {573 \ln \relax (2)}{16 \left (2+x \right )^{2}}+\frac {576 \ln \relax (2)}{2+x}-\frac {36483}{512 \left (2+x \right )^{2}}+\frac {36483}{512 \left (x -2\right )^{2}}-\frac {3}{64 \left (2+x \right )^{4}}-\frac {24 \ln \relax (2)^{3} {\mathrm e}^{x}}{2+x}+\frac {24 \ln \relax (2)^{3} {\mathrm e}^{x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{x}}{\left (2+x \right )^{2}}-\frac {297 \ln \relax (2)^{2} {\mathrm e}^{x}}{2+x}+\frac {297 \ln \relax (2)^{2} {\mathrm e}^{x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{x}}{\left (x -2\right )^{2}}+\frac {381}{128 \left (x -2\right )^{3}}+\frac {381}{128 \left (2+x \right )^{3}}+\frac {9 \ln \relax (2) {\mathrm e}^{2 x}}{\left (x -2\right )^{3}}-\frac {603 \ln \relax (2) {\mathrm e}^{2 x}}{4 \left (2+x \right )^{2}}+\frac {9 \ln \relax (2) {\mathrm e}^{2 x}}{\left (2+x \right )^{3}}+\frac {144 \ln \relax (2) {\mathrm e}^{2 x}}{x -2}+\frac {603 \ln \relax (2) {\mathrm e}^{2 x}}{4 \left (x -2\right )^{2}}+\frac {144 \ln \relax (2) {\mathrm e}^{2 x}}{2+x}+\frac {6 \ln \relax (2) {\mathrm e}^{3 x}}{\left (x -2\right )^{3}}+\frac {15 \ln \relax (2) {\mathrm e}^{3 x}}{2 \left (2+x \right )^{2}}-\frac {6 \ln \relax (2) {\mathrm e}^{3 x}}{\left (2+x \right )^{3}}+\frac {9 \ln \relax (2) {\mathrm e}^{3 x}}{4 \left (x -2\right )}+\frac {15 \ln \relax (2) {\mathrm e}^{3 x}}{2 \left (x -2\right )^{2}}-\frac {9 \ln \relax (2) {\mathrm e}^{3 x}}{4 \left (2+x \right )}-\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{\left (2+x \right )^{2}}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{\left (x -2\right )^{2}}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{2+x}-\frac {9 \,{\mathrm e}^{2 x}}{8 \left (2+x \right )^{4}}+\frac {585 \,{\mathrm e}^{2 x}}{16 \left (x -2\right )^{3}}-\frac {20151 \,{\mathrm e}^{2 x}}{64 \left (2+x \right )^{2}}+\frac {585 \,{\mathrm e}^{2 x}}{16 \left (2+x \right )^{3}}+\frac {288 \,{\mathrm e}^{2 x}}{x -2}+\frac {20151 \,{\mathrm e}^{2 x}}{64 \left (x -2\right )^{2}}+\frac {288 \,{\mathrm e}^{2 x}}{2+x}+\frac {9 \,{\mathrm e}^{2 x}}{8 \left (x -2\right )^{4}}-\frac {15 \,{\mathrm e}^{4 x}}{32 \left (2+x \right )^{2}}+\frac {9 \,{\mathrm e}^{4 x}}{8 \left (2+x \right )^{3}}+\frac {9 \,{\mathrm e}^{4 x}}{8 \left (x -2\right )^{3}}+\frac {15 \,{\mathrm e}^{4 x}}{32 \left (x -2\right )^{2}}-\frac {3 \,{\mathrm e}^{4 x}}{4 \left (2+x \right )^{4}}+\frac {3 \,{\mathrm e}^{4 x}}{4 \left (x -2\right )^{4}}+\frac {3 \,{\mathrm e}^{3 x}}{2 \left (2+x \right )^{4}}+\frac {51 \,{\mathrm e}^{3 x}}{2 \left (x -2\right )^{3}}+\frac {483 \,{\mathrm e}^{3 x}}{16 \left (2+x \right )^{2}}-\frac {51 \,{\mathrm e}^{3 x}}{2 \left (2+x \right )^{3}}+\frac {285 \,{\mathrm e}^{3 x}}{32 \left (x -2\right )}+\frac {483 \,{\mathrm e}^{3 x}}{16 \left (x -2\right )^{2}}-\frac {285 \,{\mathrm e}^{3 x}}{32 \left (2+x \right )}+\frac {3 \,{\mathrm e}^{3 x}}{2 \left (x -2\right )^{4}}+\frac {1161 \ln \relax (2) {\mathrm e}^{x}}{8 \left (2+x \right )^{2}}-\frac {9 \ln \relax (2) {\mathrm e}^{x}}{2 \left (2+x \right )^{3}}-\frac {19575 \ln \relax (2) {\mathrm e}^{x}}{16 \left (2+x \right )}+\frac {9 \ln \relax (2) {\mathrm e}^{x}}{2 \left (x -2\right )^{3}}+\frac {19575 \ln \relax (2) {\mathrm e}^{x}}{16 \left (x -2\right )}+\frac {1161 \ln \relax (2) {\mathrm e}^{x}}{8 \left (x -2\right )^{2}}\) |
\(907\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*ln(2)+288*x^8-
192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-4608*x^
3-6912*x^2)*ln(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*ln(2)+1152*x^9
-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2304*x
^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*ln(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*x^5-70272*
x^4-108288*x^3+69120*x^2+138240*x)*ln(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^4-423
360*x^3+259200*x^2+518400*x)*ln(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-550800*x^3+3
24000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*ln(2)^4+(96*x^10-1944*x^8+15552*x^6
-61440*x^4+119808*x^2-92160)*ln(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)*ln(2)^2+(1536
*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*ln(2)+1536*x^10-32256*x^8+256320*x^6-972000*x^4+176
1750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x,method=_RETURNVERBOSE)
[Out]
6*x*ln(2)^4+96*x*ln(2)^3+576*x*ln(2)^2+1536*x*ln(2)+1536*x+((24*ln(2)^3+288*ln(2)^2+1152*ln(2)+1536)*x^7+(-288
*ln(2)^3-3420*ln(2)^2-13536*ln(2)-17856)*x^5+(1152*ln(2)^3+13536*ln(2)^2+53016*ln(2)+69216)*x^3+(-1536*ln(2)^3
-17856*ln(2)^2-69216*ln(2)-89466)*x)/(x^8-16*x^6+96*x^4-256*x^2+256)+6*x^5/(x^2-4)^4*exp(4*x)+24*x^4*(x^2*ln(2
)+4*x^2-4*ln(2)-15)/(x^2-4)^4*exp(3*x)+36*x^3*(x^4*ln(2)^2+8*x^4*ln(2)-8*x^2*ln(2)^2+16*x^4-62*x^2*ln(2)+16*ln
(2)^2-120*x^2+120*ln(2)+225)/(x^2-4)^4*exp(2*x)+24*x^2*(x^6*ln(2)^3+12*x^6*ln(2)^2-12*x^4*ln(2)^3+48*x^6*ln(2)
-141*x^4*ln(2)^2+64*x^6+48*x^2*ln(2)^3-552*x^4*ln(2)+552*x^2*ln(2)^2-720*x^4-64*ln(2)^3+2115*x^2*ln(2)-720*ln(
2)^2+2700*x^2-2700*ln(2)-3375)/(x^2-4)^4*exp(x)
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maxima [B] time = 0.84, size = 1957, normalized size = 72.48 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x^5+1152*x^4+1536*x^3)*log(2)+2
88*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-
4608*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-34560*x^3-51840*x^2)*log(2)
+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x
^7+2304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8-2448*x^7+26784*x^6+28224*
x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267
840*x^4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+155520*x^5-340200*x^4-
550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*
x^8+15552*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+699840*x^2-518400)
*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^
6-972000*x^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, algorithm="maxima")
[Out]
3/64*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x
+ 2) + 315*log(x - 2))*log(2)^4 + 5/64*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 2
56*x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^4 - 1/64*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/
(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2)^4 - 5/32*(4*(15*x^7 + 292*x^
5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^4 - 5/64*
(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x -
2))*log(2)^4 - 15/32*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*log(x +
2) + 3*log(x - 2))*log(2)^4 + 3/4*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^
4 - 256*x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^3 + 81/64*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 672
0*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^3 - 15/64*(4*(105*x^7 -
1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log
(2)^3 - 81/32*(4*(15*x^7 + 292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2)
+ 15*log(x - 2))*log(2)^3 - 39/32*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 +
256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^3 - 15/2*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96
*x^4 - 256*x^2 + 256) - 3*log(x + 2) + 3*log(x - 2))*log(2)^3 + 9/2*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3
- 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^2 + 123/16*(4*(2
79*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) + 105*log(x + 2) - 105*log(x -
2))*log(2)^2 - 675/512*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) -
105*log(x + 2) + 105*log(x - 2))*log(2)^2 - 7863/512*(4*(15*x^7 + 292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 9
6*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^2 - 3645/512*(4*(15*x^7 - 220*x^5 + 1168*x^3 +
960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^2 - 22995/512*(4*(3*x^7
- 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*log(x + 2) + 3*log(x - 2))*log(2)^2 +
12*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x
+ 2) + 315*log(x - 2))*log(2) + 83/4*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*
x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2) - 3375/1024*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/
(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2) - 2647/64*(4*(15*x^7 + 292*x
^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2) - 4725/2
56*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x
- 2))*log(2) - 122175/1024*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 3*
log(x + 2) + 3*log(x - 2))*log(2) + 1536*x - 48*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*
x^4 - 256*x^2 + 256) + 84*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 5
0625/4096*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 1335/8*(15*x^7 +
292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 293625/4096*(15*x^7 - 220*x^5 + 1168*x^3
+ 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 30375/64*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6
+ 96*x^4 - 256*x^2 + 256) + 6*(x^5*e^(4*x) + 4*(x^6*(log(2) + 4) - x^4*(4*log(2) + 15))*e^(3*x) + 6*((log(2)^2
+ 8*log(2) + 16)*x^7 - 2*(4*log(2)^2 + 31*log(2) + 60)*x^5 + (16*log(2)^2 + 120*log(2) + 225)*x^3)*e^(2*x) +
4*((log(2)^3 + 12*log(2)^2 + 48*log(2) + 64)*x^8 - 3*(4*log(2)^3 + 47*log(2)^2 + 184*log(2) + 240)*x^6 + 3*(16
*log(2)^3 + 184*log(2)^2 + 705*log(2) + 900)*x^4 - (64*log(2)^3 + 720*log(2)^2 + 2700*log(2) + 3375)*x^2)*e^x)
/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^x\,\left (648000\,x+{\ln \relax (2)}^3\,\left (24\,x^{10}-384\,x^8-192\,x^7+2304\,x^6+2304\,x^5-6144\,x^4-9216\,x^3+6144\,x^2+12288\,x\right )+{\ln \relax (2)}^2\,\left (288\,x^{10}-4536\,x^8-2448\,x^7+26784\,x^6+28224\,x^5-70272\,x^4-108288\,x^3+69120\,x^2+138240\,x\right )+\ln \relax (2)\,\left (1152\,x^{10}-17856\,x^8-10368\,x^7+103752\,x^6+114912\,x^5-267840\,x^4-423360\,x^3+259200\,x^2+518400\,x\right )+324000\,x^2-550800\,x^3-340200\,x^4+155520\,x^5+133920\,x^6-14592\,x^7-23424\,x^8+1536\,x^{10}\right )+\ln \relax (2)\,\left (1536\,x^{10}-31872\,x^8+254112\,x^6-977400\,x^4+1814400\,x^2-1296000\right )+{\ln \relax (2)}^4\,\left (6\,x^{10}-120\,x^8+960\,x^6-3840\,x^4+7680\,x^2-6144\right )+{\ln \relax (2)}^3\,\left (96\,x^{10}-1944\,x^8+15552\,x^6-61440\,x^4+119808\,x^2-92160\right )+{\ln \relax (2)}^2\,\left (576\,x^{10}-11808\,x^8+94356\,x^6-367920\,x^4+699840\,x^2-518400\right )+{\mathrm {e}}^{3\,x}\,\left (\ln \relax (2)\,\left (72\,x^8-48\,x^7-576\,x^6-192\,x^5+1152\,x^4+1536\,x^3\right )+5760\,x^3+4320\,x^4-864\,x^5-2232\,x^6-192\,x^7+288\,x^8\right )-{\mathrm {e}}^{2\,x}\,\left ({\ln \relax (2)}^2\,\left (-72\,x^9+36\,x^8+864\,x^7+144\,x^6-3456\,x^5-2880\,x^4+4608\,x^3+6912\,x^2\right )+97200\,x^2+64800\,x^3-45900\,x^4-50760\,x^5+3168\,x^6+13248\,x^7+576\,x^8-1152\,x^9+\ln \relax (2)\,\left (-576\,x^9+288\,x^8+6768\,x^7+1368\,x^6-26496\,x^5-23040\,x^4+34560\,x^3+51840\,x^2\right )\right )-{\mathrm {e}}^{4\,x}\,\left (-24\,x^7+18\,x^6+96\,x^5+120\,x^4\right )+1761750\,x^2-972000\,x^4+256320\,x^6-32256\,x^8+1536\,x^{10}-1215000}{x^{10}-20\,x^8+160\,x^6-640\,x^4+1280\,x^2-1024} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 3
84*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7
- 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 -
10368*x^7 - 17856*x^8 + 1152*x^10) + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^
7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10 - 1296000)
+ log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 1555
2*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10 - 5
18400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 -
864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*
x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*
x^8 - 1152*x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x
^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24*x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 153
6*x^10 - 1215000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024),x)
[Out]
int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 3
84*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7
- 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 -
10368*x^7 - 17856*x^8 + 1152*x^10) + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^
7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10 - 1296000)
+ log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 1555
2*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10 - 5
18400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 -
864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*
x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*
x^8 - 1152*x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x
^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24*x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 153
6*x^10 - 1215000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024), x)
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sympy [B] time = 5.21, size = 1402, normalized size = 51.93 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((24*x**7-18*x**6-96*x**5-120*x**4)*exp(x)**4+((72*x**8-48*x**7-576*x**6-192*x**5+1152*x**4+1536*x**
3)*ln(2)+288*x**8-192*x**7-2232*x**6-864*x**5+4320*x**4+5760*x**3)*exp(x)**3+((72*x**9-36*x**8-864*x**7-144*x*
*6+3456*x**5+2880*x**4-4608*x**3-6912*x**2)*ln(2)**2+(576*x**9-288*x**8-6768*x**7-1368*x**6+26496*x**5+23040*x
**4-34560*x**3-51840*x**2)*ln(2)+1152*x**9-576*x**8-13248*x**7-3168*x**6+50760*x**5+45900*x**4-64800*x**3-9720
0*x**2)*exp(x)**2+((24*x**10-384*x**8-192*x**7+2304*x**6+2304*x**5-6144*x**4-9216*x**3+6144*x**2+12288*x)*ln(2
)**3+(288*x**10-4536*x**8-2448*x**7+26784*x**6+28224*x**5-70272*x**4-108288*x**3+69120*x**2+138240*x)*ln(2)**2
+(1152*x**10-17856*x**8-10368*x**7+103752*x**6+114912*x**5-267840*x**4-423360*x**3+259200*x**2+518400*x)*ln(2)
+1536*x**10-23424*x**8-14592*x**7+133920*x**6+155520*x**5-340200*x**4-550800*x**3+324000*x**2+648000*x)*exp(x)
+(6*x**10-120*x**8+960*x**6-3840*x**4+7680*x**2-6144)*ln(2)**4+(96*x**10-1944*x**8+15552*x**6-61440*x**4+11980
8*x**2-92160)*ln(2)**3+(576*x**10-11808*x**8+94356*x**6-367920*x**4+699840*x**2-518400)*ln(2)**2+(1536*x**10-3
1872*x**8+254112*x**6-977400*x**4+1814400*x**2-1296000)*ln(2)+1536*x**10-32256*x**8+256320*x**6-972000*x**4+17
61750*x**2-1215000)/(x**10-20*x**8+160*x**6-640*x**4+1280*x**2-1024),x)
[Out]
x*(6*log(2)**4 + 96*log(2)**3 + 576*log(2)**2 + 1536*log(2) + 1536) + (x**7*(24*log(2)**3 + 288*log(2)**2 + 11
52*log(2) + 1536) + x**5*(-17856 - 13536*log(2) - 3420*log(2)**2 - 288*log(2)**3) + x**3*(1152*log(2)**3 + 135
36*log(2)**2 + 53016*log(2) + 69216) + x*(-89466 - 69216*log(2) - 17856*log(2)**2 - 1536*log(2)**3))/(x**8 - 1
6*x**6 + 96*x**4 - 256*x**2 + 256) + ((6*x**29 - 288*x**27 + 6336*x**25 - 84480*x**23 + 760320*x**21 - 4866048
*x**19 + 22708224*x**17 - 77856768*x**15 + 194641920*x**13 - 346030080*x**11 + 415236096*x**9 - 301989888*x**7
+ 100663296*x**5)*exp(4*x) + (24*x**30*log(2) + 96*x**30 - 4968*x**28 - 1248*x**28*log(2) + 29952*x**26*log(2
) + 118656*x**26 - 1731840*x**24 - 439296*x**24*log(2) + 4392960*x**22*log(2) + 17233920*x**22 - 123475968*x**
20 - 31629312*x**20*log(2) + 168689664*x**18*log(2) + 655294464*x**18 - 2608201728*x**16 - 674758656*x**16*log
(2) + 2024275968*x**14*log(2) + 7785676800*x**14 - 17214996480*x**12 - 4498391040*x**12*log(2) + 7197425664*x*
*10*log(2) + 27405582336*x**10 - 29746003968*x**8 - 7851737088*x**8*log(2) + 5234491392*x**6*log(2) + 19730006
016*x**6 - 6039797760*x**4 - 1610612736*x**4*log(2))*exp(3*x) + (36*x**31*log(2)**2 + 288*x**31*log(2) + 576*x
**31 - 31968*x**29 - 16056*x**29*log(2) - 2016*x**29*log(2)**2 + 52416*x**27*log(2)**2 + 415584*x**27*log(2) +
823716*x**27 - 13060800*x**25 - 6619392*x**25*log(2) - 838656*x**25*log(2)**2 + 9225216*x**23*log(2)**2 + 724
83840*x**23*log(2) + 142369920*x**23 - 1128619008*x**21 - 577234944*x**21*log(2) - 73801728*x**21*log(2)**2 +
442810368*x**19*log(2)**2 + 3447595008*x**19*log(2) + 6709976064*x**19 - 30393335808*x**17 - 15688138752*x**17
*log(2) - 2024275968*x**17*log(2)**2 + 7084965888*x**15*log(2)**2 + 54655451136*x**15*log(2) + 105398599680*x*
*15 - 278467706880*x**13 - 145073111040*x**13*log(2) - 18893242368*x**13*log(2)**2 + 37786484736*x**11*log(2)*
*2 + 288796704768*x**11*log(2) + 551770914816*x**11 - 795101626368*x**9 - 418104999936*x**9*log(2) - 549621596
16*x**9*log(2)**2 + 54962159616*x**7*log(2)**2 + 416142065664*x**7*log(2) + 787665125376*x**7 - 480163921920*x
**5 - 254879465472*x**5*log(2) - 33822867456*x**5*log(2)**2 + 9663676416*x**3*log(2)**2 + 72477573120*x**3*log
(2) + 135895449600*x**3)*exp(2*x) + (24*x**32*log(2)**3 + 288*x**32*log(2)**2 + 1152*x**32*log(2) + 1536*x**32
- 91008*x**30 - 68544*x**30*log(2) - 17208*x**30*log(2)**2 - 1440*x**30*log(2)**3 + 40320*x**28*log(2)**3 + 4
79808*x**28*log(2)**2 + 1903176*x**28*log(2) + 2516256*x**28 - 43065960*x**26 - 32711328*x**26*log(2) - 828172
8*x**26*log(2)**2 - 698880*x**26*log(2)**3 + 8386560*x**24*log(2)**3 + 98961408*x**24*log(2)**2 + 389226240*x*
*24*log(2) + 510261120*x**24 - 4433349888*x**22 - 3396197376*x**22*log(2) - 867170304*x**22*log(2)**2 - 738017
28*x**22*log(2)**3 + 492011520*x**20*log(2)**3 + 5756534784*x**20*log(2)**2 + 22448904192*x**20*log(2) + 29179
459584*x**20 - 148148656128*x**18 - 114466480128*x**18*log(2) - 29478518784*x**18*log(2)**2 - 2530344960*x**18
*log(2)**3 + 10121379840*x**16*log(2)**3 + 117408006144*x**16*log(2)**2 + 453943885824*x**16*log(2) + 58499629
0560*x**16 - 1796566548480*x**14 - 1400124211200*x**14*log(2) - 363694915584*x**14*log(2)**2 - 31488737280*x**
14*log(2)**3 + 75572969472*x**12*log(2)**3 + 869089148928*x**12*log(2)**2 + 3331283484672*x**12*log(2) + 42560
66174976*x**12 - 7637980151808*x**10 - 6004370571264*x**10*log(2) - 1573291819008*x**10*log(2)**2 - 1374053990
40*x**10*log(2)**3 + 183207198720*x**8*log(2)**3 + 2088562065408*x**8*log(2)**2 + 7936143261696*x**8*log(2) +
10051456598016*x**8 - 9157088378880*x**6 - 7261648846848*x**6*log(2) - 1919447728128*x**6*log(2)**2 - 16911433
7280*x**6*log(2)**3 + 96636764160*x**4*log(2)**3 + 1091995435008*x**4*log(2)**2 + 4113102274560*x**4*log(2) +
5164027084800*x**4 - 1358954496000*x**2 - 1087163596800*x**2*log(2) - 289910292480*x**2*log(2)**2 - 2576980377
6*x**2*log(2)**3)*exp(x))/(x**32 - 64*x**30 + 1920*x**28 - 35840*x**26 + 465920*x**24 - 4472832*x**22 + 328007
68*x**20 - 187432960*x**18 + 843448320*x**16 - 2998927360*x**14 + 8396996608*x**12 - 18320719872*x**10 + 30534
533120*x**8 - 37580963840*x**6 + 32212254720*x**4 - 17179869184*x**2 + 4294967296)
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