3.36.9 \(\int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+(-3840 x-2304 x^2+192 x^3) \log (2)+(3840+3072 x-864 x^2) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} (24 x+36 x^2+(-48-144 x) \log (2))+e^{2 x} (240+672 x+138 x^2-36 x^3+(288 x+288 x^2) \log (2)+(-288-576 x) \log ^2(2))+e^x (-960 x-1056 x^2-144 x^3+12 x^4+(1920+3456 x+336 x^2-144 x^3) \log (2)+(1152 x+576 x^2) \log ^2(2)+(-768-768 x) \log ^3(2))}{4096} \, dx\) [3509]

Optimal. Leaf size=30 \[ -\frac {3}{16} x \left (\frac {5}{2}+x-\left (\frac {1}{4} \left (e^x-x\right )+\log (2)\right )^2\right )^2 \]

[Out]

-3/16*(x-(ln(2)-1/4*x+1/4*exp(x))^2+5/2)^2*x

________________________________________________________________________________________

Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(352\) vs. \(2(30)=60\).
time = 0.63, antiderivative size = 352, normalized size of antiderivative = 11.73, number of steps used = 74, number of rules used = 5, integrand size = 211, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6, 12, 2207, 2225, 2227} \begin {gather*} -\frac {3 x^5}{4096}+\frac {3 e^x x^4}{1024}+\frac {3 x^4}{128}+\frac {3}{256} x^4 \log (2)-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}-\frac {33 x^3}{256}-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^x x^3 \log (2)-\frac {3}{16} x^3 \log (2)-\frac {15 e^x x^2}{128}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )+\frac {9}{64} e^x x^2 \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)+\frac {3}{16} e^x x^2 \log (2)+\frac {9}{256} e^{2 x} x^2 \log (2)-\frac {15}{32} x^2 \log (2)+\frac {15}{256} e^{2 x} x+\frac {3 e^{4 x}}{16384}-\frac {3 e^{4 x} (4 x+1)}{16384}-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (x+1) \log ^3(2)+\frac {15}{16} x \log ^2(2)+\frac {9}{256} e^{2 x} \log ^2(2)-\frac {9}{256} e^{2 x} (2 x+1) \log ^2(2)+\frac {15}{32} e^x x \log (2)+\frac {1}{256} e^{3 x} \log (2)-\frac {1}{256} e^{3 x} (3 x+1) \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4800 + E^(4*x)*(-3 - 12*x) - 7680*x - 1584*x^2 + 384*x^3 - 15*x^4 + (-3840*x - 2304*x^2 + 192*x^3)*Log[2
] + (3840 + 3072*x - 864*x^2)*Log[2]^2 + 1536*x*Log[2]^3 - 768*Log[2]^4 + E^(3*x)*(24*x + 36*x^2 + (-48 - 144*
x)*Log[2]) + E^(2*x)*(240 + 672*x + 138*x^2 - 36*x^3 + (288*x + 288*x^2)*Log[2] + (-288 - 576*x)*Log[2]^2) + E
^x*(-960*x - 1056*x^2 - 144*x^3 + 12*x^4 + (1920 + 3456*x + 336*x^2 - 144*x^3)*Log[2] + (1152*x + 576*x^2)*Log
[2]^2 + (-768 - 768*x)*Log[2]^3))/4096,x]

[Out]

(3*E^(4*x))/16384 + (15*E^(2*x)*x)/256 - (15*E^x*x^2)/128 + (3*E^(2*x)*x^2)/128 + (3*E^(3*x)*x^2)/1024 - (33*x
^3)/256 - (3*E^x*x^3)/64 - (9*E^(2*x)*x^3)/2048 + (3*x^4)/128 + (3*E^x*x^4)/1024 - (3*x^5)/4096 - (3*E^(4*x)*(
1 + 4*x))/16384 + (E^(3*x)*Log[2])/256 + (15*E^x*x*Log[2])/32 - (15*x^2*Log[2])/32 + (3*E^x*x^2*Log[2])/16 + (
9*E^(2*x)*x^2*Log[2])/256 - (3*x^3*Log[2])/16 - (9*E^x*x^3*Log[2])/256 + (3*x^4*Log[2])/256 - (E^(3*x)*(1 + 3*
x)*Log[2])/256 + (9*E^(2*x)*Log[2]^2)/256 + (15*x*Log[2]^2)/16 + (3*x^2*Log[2]^2)/8 + (9*E^x*x^2*Log[2]^2)/64
- (9*x^3*Log[2]^2)/128 - (9*E^(2*x)*(1 + 2*x)*Log[2]^2)/256 + (3*E^x*Log[2]^3)/16 - (3*E^x*(1 + x)*Log[2]^3)/1
6 - (3*x^2*(5 - Log[2]^3))/16 - (3*x*(25 + 4*Log[2]^4))/64

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2207

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*
((b*F^(g*(e + f*x)))^n/(f*g*n*Log[F])), x] - Dist[d*(m/(f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !TrueQ[$UseGamma]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2227

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !TrueQ[$UseGamma]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4800+e^{4 x} (-3-12 x)-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+x \left (-7680+1536 \log ^3(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx\\ &=\frac {\int \left (-4800+e^{4 x} (-3-12 x)-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+x \left (-7680+1536 \log ^3(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )\right ) \, dx}{4096}\\ &=-\frac {33 x^3}{256}+\frac {3 x^4}{128}-\frac {3 x^5}{4096}-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {\int e^{4 x} (-3-12 x) \, dx}{4096}+\frac {\int e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right ) \, dx}{4096}+\frac {\int e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right ) \, dx}{4096}+\frac {\int e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right ) \, dx}{4096}+\frac {\log (2) \int \left (-3840 x-2304 x^2+192 x^3\right ) \, dx}{4096}+\frac {\log ^2(2) \int \left (3840+3072 x-864 x^2\right ) \, dx}{4096}\\ &=-\frac {33 x^3}{256}+\frac {3 x^4}{128}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}-\frac {15}{32} x^2 \log (2)-\frac {3}{16} x^3 \log (2)+\frac {3}{256} x^4 \log (2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {\int \left (24 e^{3 x} x+36 e^{3 x} x^2-48 e^{3 x} (1+3 x) \log (2)\right ) \, dx}{4096}+\frac {\int \left (240 e^{2 x}+672 e^{2 x} x+138 e^{2 x} x^2-36 e^{2 x} x^3+288 e^{2 x} x (1+x) \log (2)-288 e^{2 x} (1+2 x) \log ^2(2)\right ) \, dx}{4096}+\frac {\int \left (-960 e^x x-1056 e^x x^2-144 e^x x^3+12 e^x x^4-48 e^x \left (-40-72 x-7 x^2+3 x^3\right ) \log (2)+576 e^x x (2+x) \log ^2(2)-768 e^x (1+x) \log ^3(2)\right ) \, dx}{4096}+\frac {3 \int e^{4 x} \, dx}{4096}\\ &=\frac {3 e^{4 x}}{16384}-\frac {33 x^3}{256}+\frac {3 x^4}{128}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}-\frac {15}{32} x^2 \log (2)-\frac {3}{16} x^3 \log (2)+\frac {3}{256} x^4 \log (2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {3 \int e^x x^4 \, dx}{1024}+\frac {3}{512} \int e^{3 x} x \, dx+\frac {9 \int e^{3 x} x^2 \, dx}{1024}-\frac {9 \int e^{2 x} x^3 \, dx}{1024}+\frac {69 \int e^{2 x} x^2 \, dx}{2048}-\frac {9}{256} \int e^x x^3 \, dx+\frac {15}{256} \int e^{2 x} \, dx+\frac {21}{128} \int e^{2 x} x \, dx-\frac {15}{64} \int e^x x \, dx-\frac {33}{128} \int e^x x^2 \, dx-\frac {1}{256} (3 \log (2)) \int e^{3 x} (1+3 x) \, dx-\frac {1}{256} (3 \log (2)) \int e^x \left (-40-72 x-7 x^2+3 x^3\right ) \, dx+\frac {1}{128} (9 \log (2)) \int e^{2 x} x (1+x) \, dx-\frac {1}{128} \left (9 \log ^2(2)\right ) \int e^{2 x} (1+2 x) \, dx+\frac {1}{64} \left (9 \log ^2(2)\right ) \int e^x x (2+x) \, dx-\frac {1}{16} \left (3 \log ^3(2)\right ) \int e^x (1+x) \, dx\\ &=\frac {15 e^{2 x}}{512}+\frac {3 e^{4 x}}{16384}-\frac {15 e^x x}{64}+\frac {21}{256} e^{2 x} x+\frac {1}{512} e^{3 x} x-\frac {33 e^x x^2}{128}+\frac {69 e^{2 x} x^2}{4096}+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {9 e^x x^3}{256}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}-\frac {15}{32} x^2 \log (2)-\frac {3}{16} x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )-\frac {1}{512} \int e^{3 x} \, dx-\frac {3}{512} \int e^{3 x} x \, dx-\frac {3}{256} \int e^x x^3 \, dx+\frac {27 \int e^{2 x} x^2 \, dx}{2048}-\frac {69 \int e^{2 x} x \, dx}{2048}-\frac {21}{256} \int e^{2 x} \, dx+\frac {27}{256} \int e^x x^2 \, dx+\frac {15 \int e^x \, dx}{64}+\frac {33}{64} \int e^x x \, dx+\frac {1}{256} (3 \log (2)) \int e^{3 x} \, dx-\frac {1}{256} (3 \log (2)) \int \left (-40 e^x-72 e^x x-7 e^x x^2+3 e^x x^3\right ) \, dx+\frac {1}{128} (9 \log (2)) \int \left (e^{2 x} x+e^{2 x} x^2\right ) \, dx+\frac {1}{128} \left (9 \log ^2(2)\right ) \int e^{2 x} \, dx+\frac {1}{64} \left (9 \log ^2(2)\right ) \int \left (2 e^x x+e^x x^2\right ) \, dx+\frac {1}{16} \left (3 \log ^3(2)\right ) \int e^x \, dx\\ &=\frac {15 e^x}{64}-\frac {3 e^{2 x}}{256}-\frac {e^{3 x}}{1536}+\frac {3 e^{4 x}}{16384}+\frac {9 e^x x}{32}+\frac {267 e^{2 x} x}{4096}-\frac {39 e^x x^2}{256}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}+\frac {1}{256} e^{3 x} \log (2)-\frac {15}{32} x^2 \log (2)-\frac {3}{16} x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)+\frac {9}{256} e^{2 x} \log ^2(2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {1}{512} \int e^{3 x} \, dx-\frac {27 \int e^{2 x} x \, dx}{2048}+\frac {69 \int e^{2 x} \, dx}{4096}+\frac {9}{256} \int e^x x^2 \, dx-\frac {27}{128} \int e^x x \, dx-\frac {33 \int e^x \, dx}{64}-\frac {1}{256} (9 \log (2)) \int e^x x^3 \, dx+\frac {1}{128} (9 \log (2)) \int e^{2 x} x \, dx+\frac {1}{128} (9 \log (2)) \int e^{2 x} x^2 \, dx+\frac {1}{256} (21 \log (2)) \int e^x x^2 \, dx+\frac {1}{32} (15 \log (2)) \int e^x \, dx+\frac {1}{32} (27 \log (2)) \int e^x x \, dx+\frac {1}{64} \left (9 \log ^2(2)\right ) \int e^x x^2 \, dx+\frac {1}{32} \left (9 \log ^2(2)\right ) \int e^x x \, dx\\ &=-\frac {9 e^x}{32}-\frac {27 e^{2 x}}{8192}+\frac {3 e^{4 x}}{16384}+\frac {9 e^x x}{128}+\frac {15}{256} e^{2 x} x-\frac {15 e^x x^2}{128}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}+\frac {15}{32} e^x \log (2)+\frac {1}{256} e^{3 x} \log (2)+\frac {27}{32} e^x x \log (2)+\frac {9}{256} e^{2 x} x \log (2)-\frac {15}{32} x^2 \log (2)+\frac {21}{256} e^x x^2 \log (2)+\frac {9}{256} e^{2 x} x^2 \log (2)-\frac {3}{16} x^3 \log (2)-\frac {9}{256} e^x x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)+\frac {9}{256} e^{2 x} \log ^2(2)+\frac {15}{16} x \log ^2(2)+\frac {9}{32} e^x x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)+\frac {9}{64} e^x x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {27 \int e^{2 x} \, dx}{4096}-\frac {9}{128} \int e^x x \, dx+\frac {27 \int e^x \, dx}{128}-\frac {1}{256} (9 \log (2)) \int e^{2 x} \, dx-\frac {1}{128} (9 \log (2)) \int e^{2 x} x \, dx+\frac {1}{256} (27 \log (2)) \int e^x x^2 \, dx-\frac {1}{128} (21 \log (2)) \int e^x x \, dx-\frac {1}{32} (27 \log (2)) \int e^x \, dx-\frac {1}{32} \left (9 \log ^2(2)\right ) \int e^x \, dx-\frac {1}{32} \left (9 \log ^2(2)\right ) \int e^x x \, dx\\ &=-\frac {9 e^x}{128}+\frac {3 e^{4 x}}{16384}+\frac {15}{256} e^{2 x} x-\frac {15 e^x x^2}{128}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}-\frac {3}{8} e^x \log (2)-\frac {9}{512} e^{2 x} \log (2)+\frac {1}{256} e^{3 x} \log (2)+\frac {87}{128} e^x x \log (2)-\frac {15}{32} x^2 \log (2)+\frac {3}{16} e^x x^2 \log (2)+\frac {9}{256} e^{2 x} x^2 \log (2)-\frac {3}{16} x^3 \log (2)-\frac {9}{256} e^x x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)-\frac {9}{32} e^x \log ^2(2)+\frac {9}{256} e^{2 x} \log ^2(2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)+\frac {9}{64} e^x x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {9 \int e^x \, dx}{128}+\frac {1}{256} (9 \log (2)) \int e^{2 x} \, dx+\frac {1}{128} (21 \log (2)) \int e^x \, dx-\frac {1}{128} (27 \log (2)) \int e^x x \, dx+\frac {1}{32} \left (9 \log ^2(2)\right ) \int e^x \, dx\\ &=\frac {3 e^{4 x}}{16384}+\frac {15}{256} e^{2 x} x-\frac {15 e^x x^2}{128}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}-\frac {27}{128} e^x \log (2)+\frac {1}{256} e^{3 x} \log (2)+\frac {15}{32} e^x x \log (2)-\frac {15}{32} x^2 \log (2)+\frac {3}{16} e^x x^2 \log (2)+\frac {9}{256} e^{2 x} x^2 \log (2)-\frac {3}{16} x^3 \log (2)-\frac {9}{256} e^x x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)+\frac {9}{256} e^{2 x} \log ^2(2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)+\frac {9}{64} e^x x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )+\frac {1}{128} (27 \log (2)) \int e^x \, dx\\ &=\frac {3 e^{4 x}}{16384}+\frac {15}{256} e^{2 x} x-\frac {15 e^x x^2}{128}+\frac {3}{128} e^{2 x} x^2+\frac {3 e^{3 x} x^2}{1024}-\frac {33 x^3}{256}-\frac {3 e^x x^3}{64}-\frac {9 e^{2 x} x^3}{2048}+\frac {3 x^4}{128}+\frac {3 e^x x^4}{1024}-\frac {3 x^5}{4096}-\frac {3 e^{4 x} (1+4 x)}{16384}+\frac {1}{256} e^{3 x} \log (2)+\frac {15}{32} e^x x \log (2)-\frac {15}{32} x^2 \log (2)+\frac {3}{16} e^x x^2 \log (2)+\frac {9}{256} e^{2 x} x^2 \log (2)-\frac {3}{16} x^3 \log (2)-\frac {9}{256} e^x x^3 \log (2)+\frac {3}{256} x^4 \log (2)-\frac {1}{256} e^{3 x} (1+3 x) \log (2)+\frac {9}{256} e^{2 x} \log ^2(2)+\frac {15}{16} x \log ^2(2)+\frac {3}{8} x^2 \log ^2(2)+\frac {9}{64} e^x x^2 \log ^2(2)-\frac {9}{128} x^3 \log ^2(2)-\frac {9}{256} e^{2 x} (1+2 x) \log ^2(2)+\frac {3}{16} e^x \log ^3(2)-\frac {3}{16} e^x (1+x) \log ^3(2)-\frac {3}{16} x^2 \left (5-\log ^3(2)\right )-\frac {3}{64} x \left (25+4 \log ^4(2)\right )\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(119\) vs. \(2(30)=60\).
time = 0.32, size = 119, normalized size = 3.97 \begin {gather*} -\frac {3 x \left (e^{4 x}-4 e^{3 x} (x-4 \log (2))+\left (x^2-8 x (2+\log (2))+8 \left (-5+2 \log ^2(2)\right )\right )^2-4 e^x \left (x^3-4 x^2 (4+\log (8))-8 \left (-27 \log (2)+8 \log ^3(2)+\log (128)\right )+4 x \left (-10+12 \log ^2(2)+\log (65536)\right )\right )+e^{2 x} \left (-80+6 x^2+96 \log ^2(2)-2 x (16+\log (16777216))\right )\right )}{4096} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4800 + E^(4*x)*(-3 - 12*x) - 7680*x - 1584*x^2 + 384*x^3 - 15*x^4 + (-3840*x - 2304*x^2 + 192*x^3)
*Log[2] + (3840 + 3072*x - 864*x^2)*Log[2]^2 + 1536*x*Log[2]^3 - 768*Log[2]^4 + E^(3*x)*(24*x + 36*x^2 + (-48
- 144*x)*Log[2]) + E^(2*x)*(240 + 672*x + 138*x^2 - 36*x^3 + (288*x + 288*x^2)*Log[2] + (-288 - 576*x)*Log[2]^
2) + E^x*(-960*x - 1056*x^2 - 144*x^3 + 12*x^4 + (1920 + 3456*x + 336*x^2 - 144*x^3)*Log[2] + (1152*x + 576*x^
2)*Log[2]^2 + (-768 - 768*x)*Log[2]^3))/4096,x]

[Out]

(-3*x*(E^(4*x) - 4*E^(3*x)*(x - 4*Log[2]) + (x^2 - 8*x*(2 + Log[2]) + 8*(-5 + 2*Log[2]^2))^2 - 4*E^x*(x^3 - 4*
x^2*(4 + Log[8]) - 8*(-27*Log[2] + 8*Log[2]^3 + Log[128]) + 4*x*(-10 + 12*Log[2]^2 + Log[65536])) + E^(2*x)*(-
80 + 6*x^2 + 96*Log[2]^2 - 2*x*(16 + Log[16777216]))))/4096

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(224\) vs. \(2(22)=44\).
time = 0.46, size = 225, normalized size = 7.50

method	result	size
norman	\(\left (\frac {3 \ln \left (2\right )}{256}+\frac {3}{128}\right ) x^{4}+\left (-\frac {9 \ln \left (2\right )^{2}}{128}-\frac {3 \ln \left (2\right )}{16}-\frac {33}{256}\right ) x^{3}+\left (-\frac {3 \ln \left (2\right )^{4}}{16}+\frac {15 \ln \left (2\right )^{2}}{16}-\frac {75}{64}\right ) x +\left (\frac {3 \ln \left (2\right )^{3}}{16}+\frac {3 \ln \left (2\right )^{2}}{8}-\frac {15 \ln \left (2\right )}{32}-\frac {15}{16}\right ) x^{2}+\left (-\frac {3}{64}-\frac {9 \ln \left (2\right )}{256}\right ) x^{3} {\mathrm e}^{x}+\left (\frac {3}{128}+\frac {9 \ln \left (2\right )}{256}\right ) x^{2} {\mathrm e}^{2 x}+\left (\frac {15}{256}-\frac {9 \ln \left (2\right )^{2}}{128}\right ) x \,{\mathrm e}^{2 x}+\left (-\frac {3 \ln \left (2\right )^{3}}{16}+\frac {15 \ln \left (2\right )}{32}\right ) x \,{\mathrm e}^{x}+\left (-\frac {15}{128}+\frac {3 \ln \left (2\right )}{16}+\frac {9 \ln \left (2\right )^{2}}{64}\right ) x^{2} {\mathrm e}^{x}-\frac {3 x^{5}}{4096}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}-\frac {3 x \ln \left (2\right ) {\mathrm e}^{3 x}}{256}\)	\(185\)
risch	\(-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {\left (-48 x \ln \left (2\right )+12 x^{2}\right ) {\mathrm e}^{3 x}}{4096}+\frac {\left (-288 x \ln \left (2\right )^{2}+144 x^{2} \ln \left (2\right )-18 x^{3}+96 x^{2}+240 x \right ) {\mathrm e}^{2 x}}{4096}+\frac {\left (-768 x \ln \left (2\right )^{3}+576 x^{2} \ln \left (2\right )^{2}-144 x^{3} \ln \left (2\right )+12 x^{4}+768 x^{2} \ln \left (2\right )-192 x^{3}+1920 x \ln \left (2\right )-480 x^{2}\right ) {\mathrm e}^{x}}{4096}-\frac {3 x \ln \left (2\right )^{4}}{16}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {9 x^{3} \ln \left (2\right )^{2}}{128}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {15 x \ln \left (2\right )^{2}}{16}+\frac {3 x^{4} \ln \left (2\right )}{256}-\frac {3 x^{3} \ln \left (2\right )}{16}-\frac {15 x^{2} \ln \left (2\right )}{32}-\frac {3 x^{5}}{4096}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}-\frac {75 x}{64}\)	\(200\)
default	\(-\frac {75 x}{64}+\frac {3 x^{2} \ln \left (2\right ) {\mathrm e}^{x}}{16}-\frac {9 x^{3} \ln \left (2\right ) {\mathrm e}^{x}}{256}-\frac {9 x \ln \left (2\right )^{2} {\mathrm e}^{2 x}}{128}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {3 x \ln \left (2\right )^{4}}{16}-\frac {9 x^{3} \ln \left (2\right )^{2}}{128}+\frac {3 \,{\mathrm e}^{2 x} x^{2}}{128}+\frac {15 x \,{\mathrm e}^{2 x}}{256}+\frac {15 x \ln \left (2\right )^{2}}{16}+\frac {3 x^{4} \ln \left (2\right )}{256}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {3 \,{\mathrm e}^{x} x^{3}}{64}-\frac {15 x^{2} \ln \left (2\right )}{32}-\frac {3 x^{3} \ln \left (2\right )}{16}-\frac {15 \,{\mathrm e}^{x} x^{2}}{128}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {15 x \ln \left (2\right ) {\mathrm e}^{x}}{32}-\frac {3 x^{5}}{4096}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}+\frac {9 x^{2} \ln \left (2\right ) {\mathrm e}^{2 x}}{256}+\frac {9 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{2}}{64}-\frac {3 \,{\mathrm e}^{x} \ln \left (2\right )^{3} x}{16}-\frac {3 x \ln \left (2\right ) {\mathrm e}^{3 x}}{256}\)	\(225\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*ln(2)+36*x^2+24*x)*exp(x)^3+1/4096*((-576*x-288)*ln(2)^2+(28
8*x^2+288*x)*ln(2)-36*x^3+138*x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*ln(2)^3+(576*x^2+1152*x)*ln(2)^2+(-
144*x^3+336*x^2+3456*x+1920)*ln(2)+12*x^4-144*x^3-1056*x^2-960*x)*exp(x)-3/16*ln(2)^4+3/8*x*ln(2)^3+1/4096*(-8
64*x^2+3072*x+3840)*ln(2)^2+1/4096*(192*x^3-2304*x^2-3840*x)*ln(2)-15/4096*x^4+3/32*x^3-99/256*x^2-15/8*x-75/6
4,x,method=_RETURNVERBOSE)

[Out]

-75/64*x+3/16*x^2*ln(2)*exp(x)+9/256*x^2*ln(2)*exp(x)^2-9/128*x*ln(2)^2*exp(x)^2-9/256*x^3*ln(2)*exp(x)-3/256*
x*ln(2)*exp(x)^3+3/16*x^2*ln(2)^3-3/16*x*ln(2)^4+3/1024*x^2*exp(x)^3-9/128*x^3*ln(2)^2+15/16*x*ln(2)^2+3/256*x
^4*ln(2)+3/8*x^2*ln(2)^2+3/1024*exp(x)*x^4+15/256*x*exp(x)^2+3/128*exp(x)^2*x^2-3/64*exp(x)*x^3-15/32*x^2*ln(2
)-3/16*x^3*ln(2)-15/128*exp(x)*x^2-3/4096*x*exp(x)^4-9/2048*exp(x)^2*x^3+15/32*x*ln(2)*exp(x)-3/4096*x^5+3/128
*x^4-33/256*x^3-15/16*x^2+9/64*exp(x)*ln(2)^2*x^2-3/16*exp(x)*ln(2)^3*x

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 184 vs. \(2 (22) = 44\).
time = 0.47, size = 184, normalized size = 6.13 \begin {gather*} -\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 8 \, x^{2} {\left (3 \, \log \left (2\right ) + 2\right )} + 8 \, {\left (6 \, \log \left (2\right )^{2} - 5\right )} x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} - 4 \, x^{3} {\left (3 \, \log \left (2\right ) + 4\right )} + 8 \, {\left (6 \, \log \left (2\right )^{2} + 8 \, \log \left (2\right ) - 5\right )} x^{2} - 32 \, {\left (2 \, \log \left (2\right )^{3} - 5 \, \log \left (2\right )\right )} x\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x)*exp(x)^3+1/4096*((-576*x-288)*log(
2)^2+(288*x^2+288*x)*log(2)-36*x^3+138*x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*
log(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x)*exp(x)-3/16*log(2)^4+3/8*x*log(2
)^3+1/4096*(-864*x^2+3072*x+3840)*log(2)^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256
*x^2-15/8*x-75/64,x, algorithm="maxima")

[Out]

-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log
(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 8*x^2*(3*log(2) + 2
) + 8*(6*log(2)^2 - 5)*x)*e^(2*x) + 3/1024*(x^4 - 4*x^3*(3*log(2) + 4) + 8*(6*log(2)^2 + 8*log(2) - 5)*x^2 - 3
2*(2*log(2)^3 - 5*log(2))*x)*e^x + 3/256*(x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 186 vs. \(2 (22) = 44\).
time = 0.37, size = 186, normalized size = 6.20 \begin {gather*} -\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 24 \, x^{2} \log \left (2\right ) + 48 \, x \log \left (2\right )^{2} - 16 \, x^{2} - 40 \, x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} + 48 \, x^{2} \log \left (2\right )^{2} - 64 \, x \log \left (2\right )^{3} - 16 \, x^{3} - 40 \, x^{2} - 4 \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x)*exp(x)^3+1/4096*((-576*x-288)*log(
2)^2+(288*x^2+288*x)*log(2)-36*x^3+138*x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*
log(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x)*exp(x)-3/16*log(2)^4+3/8*x*log(2
)^3+1/4096*(-864*x^2+3072*x+3840)*log(2)^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256
*x^2-15/8*x-75/64,x, algorithm="fricas")

[Out]

-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log
(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 24*x^2*log(2) + 48*
x*log(2)^2 - 16*x^2 - 40*x)*e^(2*x) + 3/1024*(x^4 + 48*x^2*log(2)^2 - 64*x*log(2)^3 - 16*x^3 - 40*x^2 - 4*(3*x
^3 - 16*x^2 - 40*x)*log(2))*e^x + 3/256*(x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 224 vs. \(2 (26) = 52\).
time = 0.22, size = 224, normalized size = 7.47 \begin {gather*} - \frac {3 x^{5}}{4096} + x^{4} \cdot \left (\frac {3 \log {\left (2 \right )}}{256} + \frac {3}{128}\right ) + x^{3} \left (- \frac {3 \log {\left (2 \right )}}{16} - \frac {33}{256} - \frac {9 \log {\left (2 \right )}^{2}}{128}\right ) + x^{2} \left (- \frac {15}{16} - \frac {15 \log {\left (2 \right )}}{32} + \frac {3 \log {\left (2 \right )}^{3}}{16} + \frac {3 \log {\left (2 \right )}^{2}}{8}\right ) - \frac {3 x e^{4 x}}{4096} + x \left (- \frac {75}{64} - \frac {3 \log {\left (2 \right )}^{4}}{16} + \frac {15 \log {\left (2 \right )}^{2}}{16}\right ) + \frac {\left (25769803776 x^{2} - 103079215104 x \log {\left (2 \right )}\right ) e^{3 x}}{8796093022208} + \frac {\left (- 38654705664 x^{3} + 206158430208 x^{2} + 309237645312 x^{2} \log {\left (2 \right )} - 618475290624 x \log {\left (2 \right )}^{2} + 515396075520 x\right ) e^{2 x}}{8796093022208} + \frac {\left (25769803776 x^{4} - 412316860416 x^{3} - 309237645312 x^{3} \log {\left (2 \right )} - 1030792151040 x^{2} + 1236950581248 x^{2} \log {\left (2 \right )}^{2} + 1649267441664 x^{2} \log {\left (2 \right )} - 1649267441664 x \log {\left (2 \right )}^{3} + 4123168604160 x \log {\left (2 \right )}\right ) e^{x}}{8796093022208} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4096*(-12*x-3)*exp(x)**4+1/4096*((-144*x-48)*ln(2)+36*x**2+24*x)*exp(x)**3+1/4096*((-576*x-288)*ln
(2)**2+(288*x**2+288*x)*ln(2)-36*x**3+138*x**2+672*x+240)*exp(x)**2+1/4096*((-768*x-768)*ln(2)**3+(576*x**2+11
52*x)*ln(2)**2+(-144*x**3+336*x**2+3456*x+1920)*ln(2)+12*x**4-144*x**3-1056*x**2-960*x)*exp(x)-3/16*ln(2)**4+3
/8*x*ln(2)**3+1/4096*(-864*x**2+3072*x+3840)*ln(2)**2+1/4096*(192*x**3-2304*x**2-3840*x)*ln(2)-15/4096*x**4+3/
32*x**3-99/256*x**2-15/8*x-75/64,x)

[Out]

-3*x**5/4096 + x**4*(3*log(2)/256 + 3/128) + x**3*(-3*log(2)/16 - 33/256 - 9*log(2)**2/128) + x**2*(-15/16 - 1
5*log(2)/32 + 3*log(2)**3/16 + 3*log(2)**2/8) - 3*x*exp(4*x)/4096 + x*(-75/64 - 3*log(2)**4/16 + 15*log(2)**2/
16) + (25769803776*x**2 - 103079215104*x*log(2))*exp(3*x)/8796093022208 + (-38654705664*x**3 + 206158430208*x*
*2 + 309237645312*x**2*log(2) - 618475290624*x*log(2)**2 + 515396075520*x)*exp(2*x)/8796093022208 + (257698037
76*x**4 - 412316860416*x**3 - 309237645312*x**3*log(2) - 1030792151040*x**2 + 1236950581248*x**2*log(2)**2 + 1
649267441664*x**2*log(2) - 1649267441664*x*log(2)**3 + 4123168604160*x*log(2))*exp(x)/8796093022208

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (22) = 44\).
time = 0.41, size = 187, normalized size = 6.23 \begin {gather*} -\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 24 \, x^{2} \log \left (2\right ) + 48 \, x \log \left (2\right )^{2} - 16 \, x^{2} - 40 \, x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} - 12 \, x^{3} \log \left (2\right ) + 48 \, x^{2} \log \left (2\right )^{2} - 64 \, x \log \left (2\right )^{3} - 16 \, x^{3} + 64 \, x^{2} \log \left (2\right ) - 40 \, x^{2} + 160 \, x \log \left (2\right )\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x)*exp(x)^3+1/4096*((-576*x-288)*log(
2)^2+(288*x^2+288*x)*log(2)-36*x^3+138*x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*
log(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x)*exp(x)-3/16*log(2)^4+3/8*x*log(2
)^3+1/4096*(-864*x^2+3072*x+3840)*log(2)^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256
*x^2-15/8*x-75/64,x, algorithm="giac")

[Out]

-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log
(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 24*x^2*log(2) + 48*
x*log(2)^2 - 16*x^2 - 40*x)*e^(2*x) + 3/1024*(x^4 - 12*x^3*log(2) + 48*x^2*log(2)^2 - 64*x*log(2)^3 - 16*x^3 +
64*x^2*log(2) - 40*x^2 + 160*x*log(2))*e^x + 3/256*(x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x

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Mupad [B]
time = 2.33, size = 43, normalized size = 1.43 \begin {gather*} -\frac {3\,x\,{\left (16\,x-{\mathrm {e}}^{2\,x}+8\,x\,\ln \left (2\right )-8\,{\mathrm {e}}^x\,\ln \left (2\right )+2\,x\,{\mathrm {e}}^x-16\,{\ln \left (2\right )}^2-x^2+40\right )}^2}{4096} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3*x)*(24*x - log(2)*(144*x + 48) + 36*x^2))/4096 - (15*x)/8 - (log(2)*(3840*x + 2304*x^2 - 192*x^3))/
4096 - (exp(x)*(960*x + log(2)^3*(768*x + 768) - log(2)*(3456*x + 336*x^2 - 144*x^3 + 1920) - log(2)^2*(1152*x
+ 576*x^2) + 1056*x^2 + 144*x^3 - 12*x^4))/4096 + (log(2)^2*(3072*x - 864*x^2 + 3840))/4096 + (3*x*log(2)^3)/
8 - (3*log(2)^4)/16 - (exp(4*x)*(12*x + 3))/4096 - (99*x^2)/256 + (3*x^3)/32 - (15*x^4)/4096 + (exp(2*x)*(672*
x + log(2)*(288*x + 288*x^2) - log(2)^2*(576*x + 288) + 138*x^2 - 36*x^3 + 240))/4096 - 75/64,x)

[Out]

-(3*x*(16*x - exp(2*x) + 8*x*log(2) - 8*exp(x)*log(2) + 2*x*exp(x) - 16*log(2)^2 - x^2 + 40)^2)/4096

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