3.4.26 \(\int (-1+9600 e^2 x+2000 e x^2+100 x^3+e^{2+2 x} (800 x+800 x^2)+(5600 e^2 x+600 e x^2) \log (5)+800 e^2 x \log ^2(5)+e^x (e^2 (5600 x+2400 x^2)+e (600 x^2+200 x^3)+e^2 (1600 x+800 x^2) \log (5))+(5600 e^2 x+600 e x^2+e^{2+x} (1600 x+800 x^2)+1600 e^2 x \log (5)) \log (x)+800 e^2 x \log ^2(x)) \, dx\) [326]

Optimal. Leaf size=25 \[ -x+25 x^2 \left (x+4 e \left (3+e^x+\log (5)+\log (x)\right )\right )^2 \]

[Out]

5*x^2*(4*(exp(x)+ln(x)+ln(5)+3)*exp(1)+x)*(20*(exp(x)+ln(x)+ln(5)+3)*exp(1)+5*x)-x

________________________________________________________________________________________

Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(167\) vs. \(2(25)=50\).
time = 0.33, antiderivative size = 167, normalized size of antiderivative = 6.68, number of steps used = 47, number of rules used = 11, integrand size = 157, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {6, 1607, 2227, 2207, 2225, 2634, 12, 14, 45, 2342, 2341} \begin {gather*} 25 x^4+200 e^{x+1} x^3+600 e x^3+200 e x^3 \log (x)+200 e x^3 \log (5)+2400 e^{x+2} x^2+400 e^{2 x+2} x^2+200 e^2 x^2+400 e^2 x^2 \log ^2(x)+400 e^2 x^2 \left (12+\log ^2(5)\right )+800 e^{x+2} x^2 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)-400 e^2 x^2 \log (x)-200 e^2 x^2 (7+\log (25))+800 e^{x+2} x^2 \log (5)+2800 e^2 x^2 \log (5)-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + 9600*E^2*x + 2000*E*x^2 + 100*x^3 + E^(2 + 2*x)*(800*x + 800*x^2) + (5600*E^2*x + 600*E*x^2)*Log[5] +
800*E^2*x*Log[5]^2 + E^x*(E^2*(5600*x + 2400*x^2) + E*(600*x^2 + 200*x^3) + E^2*(1600*x + 800*x^2)*Log[5]) +
(5600*E^2*x + 600*E*x^2 + E^(2 + x)*(1600*x + 800*x^2) + 1600*E^2*x*Log[5])*Log[x] + 800*E^2*x*Log[x]^2,x]

[Out]

-x + 200*E^2*x^2 + 2400*E^(2 + x)*x^2 + 400*E^(2 + 2*x)*x^2 + 600*E*x^3 + 200*E^(1 + x)*x^3 + 25*x^4 + 2800*E^
2*x^2*Log[5] + 800*E^(2 + x)*x^2*Log[5] + 200*E*x^3*Log[5] + 400*E^2*x^2*(12 + Log[5]^2) - 200*E^2*x^2*(7 + Lo
g[25]) - 400*E^2*x^2*Log[x] + 800*E^(2 + x)*x^2*Log[x] + 200*E*x^3*Log[x] + 400*E^2*x^2*(7 + Log[25])*Log[x] +
400*E^2*x^2*Log[x]^2

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 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 1607

Int[(u_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(n*p)*(a + b*x^(q - p))^n, x] /; F
reeQ[{a, b, p, q}, x] && IntegerQ[n] && PosQ[q - p]

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]

Rule 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2342

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Lo
g[c*x^n])^p/(d*(m + 1))), x] - Dist[b*n*(p/(m + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2634

Int[Log[u_]*(v_), x_Symbol] :> With[{w = IntHide[v, x]}, Dist[Log[u], w, x] - Int[SimplifyIntegrand[w*(D[u, x]
/u), x], x] /; InverseFunctionFreeQ[w, x]] /; InverseFunctionFreeQ[u, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+2000 e x^2+100 x^3+e^{2+2 x} \left (800 x+800 x^2\right )+\left (5600 e^2 x+600 e x^2\right ) \log (5)+e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right )+e^2 x \left (9600+800 \log ^2(5)\right )+\left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x)+800 e^2 x \log ^2(x)\right ) \, dx\\ &=-x+\frac {2000 e x^3}{3}+25 x^4+400 e^2 x^2 \left (12+\log ^2(5)\right )+\left (800 e^2\right ) \int x \log ^2(x) \, dx+\log (5) \int \left (5600 e^2 x+600 e x^2\right ) \, dx+\int e^{2+2 x} \left (800 x+800 x^2\right ) \, dx+\int e^x \left (e^2 \left (5600 x+2400 x^2\right )+e \left (600 x^2+200 x^3\right )+e^2 \left (1600 x+800 x^2\right ) \log (5)\right ) \, dx+\int \left (5600 e^2 x+600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+1600 e^2 x \log (5)\right ) \log (x) \, dx\\ &=-x+\frac {2000 e x^3}{3}+25 x^4+2800 e^2 x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )+400 e^2 x^2 \log ^2(x)-\left (800 e^2\right ) \int x \log (x) \, dx+\int e^{2+2 x} x (800+800 x) \, dx+\int \left (200 e^{1+x} x^2 (3+x)+800 e^{2+x} x (7+3 x)+800 e^{2+x} x (2+x) \log (5)\right ) \, dx+\int \left (600 e x^2+e^{2+x} \left (1600 x+800 x^2\right )+e^2 x (5600+1600 \log (5))\right ) \log (x) \, dx\\ &=-x+200 e^2 x^2+\frac {2000 e x^3}{3}+25 x^4+2800 e^2 x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)+200 \int e^{1+x} x^2 (3+x) \, dx+800 \int e^{2+x} x (7+3 x) \, dx+(800 \log (5)) \int e^{2+x} x (2+x) \, dx+\int \left (800 e^{2+2 x} x+800 e^{2+2 x} x^2\right ) \, dx-\int 200 e x \left (4 e^{1+x}+x+2 e (7+\log (25))\right ) \, dx\\ &=-x+200 e^2 x^2+\frac {2000 e x^3}{3}+25 x^4+2800 e^2 x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)+200 \int \left (3 e^{1+x} x^2+e^{1+x} x^3\right ) \, dx+800 \int e^{2+2 x} x \, dx+800 \int e^{2+2 x} x^2 \, dx+800 \int \left (7 e^{2+x} x+3 e^{2+x} x^2\right ) \, dx-(200 e) \int x \left (4 e^{1+x}+x+2 e (7+\log (25))\right ) \, dx+(800 \log (5)) \int \left (2 e^{2+x} x+e^{2+x} x^2\right ) \, dx\\ &=-x+400 e^{2+2 x} x+200 e^2 x^2+400 e^{2+2 x} x^2+\frac {2000 e x^3}{3}+25 x^4+2800 e^2 x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)+200 \int e^{1+x} x^3 \, dx-400 \int e^{2+2 x} \, dx+600 \int e^{1+x} x^2 \, dx-800 \int e^{2+2 x} x \, dx+2400 \int e^{2+x} x^2 \, dx+5600 \int e^{2+x} x \, dx-(200 e) \int \left (4 e^{1+x} x+x (14 e+x+2 e \log (25))\right ) \, dx+(800 \log (5)) \int e^{2+x} x^2 \, dx+(1600 \log (5)) \int e^{2+x} x \, dx\\ &=-200 e^{2+2 x}-x+5600 e^{2+x} x+200 e^2 x^2+600 e^{1+x} x^2+2400 e^{2+x} x^2+400 e^{2+2 x} x^2+\frac {2000 e x^3}{3}+200 e^{1+x} x^3+25 x^4+1600 e^{2+x} x \log (5)+2800 e^2 x^2 \log (5)+800 e^{2+x} x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)+400 \int e^{2+2 x} \, dx-600 \int e^{1+x} x^2 \, dx-1200 \int e^{1+x} x \, dx-4800 \int e^{2+x} x \, dx-5600 \int e^{2+x} \, dx-(200 e) \int x (14 e+x+2 e \log (25)) \, dx-(800 e) \int e^{1+x} x \, dx-(1600 \log (5)) \int e^{2+x} \, dx-(1600 \log (5)) \int e^{2+x} x \, dx\\ &=-5600 e^{2+x}-x-1200 e^{1+x} x+200 e^2 x^2+2400 e^{2+x} x^2+400 e^{2+2 x} x^2+\frac {2000 e x^3}{3}+200 e^{1+x} x^3+25 x^4-1600 e^{2+x} \log (5)+2800 e^2 x^2 \log (5)+800 e^{2+x} x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)+1200 \int e^{1+x} \, dx+1200 \int e^{1+x} x \, dx+4800 \int e^{2+x} \, dx-(200 e) \int \left (x^2+2 e x (7+\log (25))\right ) \, dx+(800 e) \int e^{1+x} \, dx+(1600 \log (5)) \int e^{2+x} \, dx\\ &=1200 e^{1+x}-x+200 e^2 x^2+2400 e^{2+x} x^2+400 e^{2+2 x} x^2+600 e x^3+200 e^{1+x} x^3+25 x^4+2800 e^2 x^2 \log (5)+800 e^{2+x} x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-200 e^2 x^2 (7+\log (25))-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)-1200 \int e^{1+x} \, dx\\ &=-x+200 e^2 x^2+2400 e^{2+x} x^2+400 e^{2+2 x} x^2+600 e x^3+200 e^{1+x} x^3+25 x^4+2800 e^2 x^2 \log (5)+800 e^{2+x} x^2 \log (5)+200 e x^3 \log (5)+400 e^2 x^2 \left (12+\log ^2(5)\right )-200 e^2 x^2 (7+\log (25))-400 e^2 x^2 \log (x)+800 e^{2+x} x^2 \log (x)+200 e x^3 \log (x)+400 e^2 x^2 (7+\log (25)) \log (x)+400 e^2 x^2 \log ^2(x)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(25)=50\).
time = 0.22, size = 102, normalized size = 4.08 \begin {gather*} \frac {1}{3} x \left (-3+1200 e^{2+2 x} x+600 e^{1+x} x^2+75 x^3+2400 e^{2+x} x (3+\log (5))+200 e x^2 (9+\log (125))+600 e^2 x \left (18+2 \log ^2(5)+\log (244140625)\right )+600 e x \left (4 e^{1+x}+x+2 e (6+\log (25))\right ) \log (x)+1200 e^2 x \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + 9600*E^2*x + 2000*E*x^2 + 100*x^3 + E^(2 + 2*x)*(800*x + 800*x^2) + (5600*E^2*x + 600*E*x^2)*Lo
g[5] + 800*E^2*x*Log[5]^2 + E^x*(E^2*(5600*x + 2400*x^2) + E*(600*x^2 + 200*x^3) + E^2*(1600*x + 800*x^2)*Log[
5]) + (5600*E^2*x + 600*E*x^2 + E^(2 + x)*(1600*x + 800*x^2) + 1600*E^2*x*Log[5])*Log[x] + 800*E^2*x*Log[x]^2,
x]

[Out]

(x*(-3 + 1200*E^(2 + 2*x)*x + 600*E^(1 + x)*x^2 + 75*x^3 + 2400*E^(2 + x)*x*(3 + Log[5]) + 200*E*x^2*(9 + Log[
125]) + 600*E^2*x*(18 + 2*Log[5]^2 + Log[244140625]) + 600*E*x*(4*E^(1 + x) + x + 2*E*(6 + Log[25]))*Log[x] +
1200*E^2*x*Log[x]^2))/3

________________________________________________________________________________________

Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(163\) vs. \(2(39)=78\).
time = 0.18, size = 164, normalized size = 6.56

method	result	size
risch	\(-x +2400 \ln \left (5\right ) {\mathrm e}^{2} x^{2}+200 \ln \left (5\right ) {\mathrm e} x^{3}+200 x^{3} {\mathrm e}^{x +1}+2400 x^{2} {\mathrm e}^{2+x}+800 x^{2} \ln \left (5\right ) {\mathrm e}^{2+x}+800 \,{\mathrm e}^{2} \ln \left (5\right ) x^{2} \ln \left (x \right )+2400 x^{2} {\mathrm e}^{2} \ln \left (x \right )+3600 x^{2} {\mathrm e}^{2}+200 x^{3} {\mathrm e} \ln \left (x \right )+600 x^{3} {\mathrm e}+800 x^{2} \ln \left (x \right ) {\mathrm e}^{2+x}+400 x^{2} {\mathrm e}^{2 x +2}+25 x^{4}+400 x^{2} {\mathrm e}^{2} \ln \left (5\right )^{2}+400 \,{\mathrm e}^{2} \ln \left (x \right )^{2} x^{2}\)	\(144\)
default	\(-x +2400 \ln \left (5\right ) {\mathrm e}^{2} x^{2}+200 \ln \left (5\right ) {\mathrm e} x^{3}+200 x^{3} {\mathrm e} \,{\mathrm e}^{x}+2400 x^{2} {\mathrm e}^{2} {\mathrm e}^{x}+800 \ln \left (5\right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+800 \,{\mathrm e}^{2} \ln \left (5\right ) x^{2} \ln \left (x \right )+2400 x^{2} {\mathrm e}^{2} \ln \left (x \right )+3600 x^{2} {\mathrm e}^{2}+200 x^{3} {\mathrm e} \ln \left (x \right )+600 x^{3} {\mathrm e}+800 \ln \left (x \right ) {\mathrm e}^{2} {\mathrm e}^{x} x^{2}+400 x^{2} {\mathrm e}^{2} {\mathrm e}^{2 x}+25 x^{4}+400 x^{2} {\mathrm e}^{2} \ln \left (5\right )^{2}+400 \,{\mathrm e}^{2} \ln \left (x \right )^{2} x^{2}\)	\(164\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(800*x*exp(1)^2*ln(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x*exp(1)^2*ln(5)+5600*x*exp(1)^2+600*x^2*exp
(1))*ln(x)+(800*x^2+800*x)*exp(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*ln(5)+(2400*x^2+5600*x)*exp(1)^2+(200*
x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*ln(5)^2+(5600*x*exp(1)^2+600*x^2*exp(1))*ln(5)+9600*x*exp(1)^2+2000
*x^2*exp(1)+100*x^3-1,x,method=_RETURNVERBOSE)

[Out]

-x+2400*ln(5)*exp(1)^2*x^2+200*ln(5)*exp(1)*x^3+200*x^3*exp(1)*exp(x)+2400*x^2*exp(1)^2*exp(x)+800*ln(5)*exp(1
)^2*exp(x)*x^2+800*exp(1)^2*ln(5)*x^2*ln(x)+2400*exp(1)^2*x^2*ln(x)+3600*x^2*exp(1)^2+200*x^3*exp(1)*ln(x)+600
*x^3*exp(1)+800*ln(x)*exp(1)^2*exp(x)*x^2+400*exp(1)^2*exp(x)^2*x^2+25*x^4+400*x^2*exp(1)^2*ln(5)^2+400*exp(1)
^2*ln(x)^2*x^2

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 175 vs. \(2 (25) = 50\).
time = 0.52, size = 175, normalized size = 7.00 \begin {gather*} 400 \, x^{2} e^{2} \log \left (5\right )^{2} + 25 \, x^{4} + 200 \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} e^{2} - 200 \, x^{2} {\left (2 \, \log \left (5\right ) + 7\right )} e^{2} + 600 \, x^{3} e + 4800 \, x^{2} e^{2} + 400 \, x^{2} e^{\left (2 \, x + 2\right )} + 200 \, {\left (4 \, x^{2} {\left (\log \left (5\right ) + 3\right )} e^{2} + x^{3} e + 4 \, x e^{2} - 4 \, e^{2}\right )} e^{x} - 800 \, {\left (x e^{2} - e^{2}\right )} e^{x} + 200 \, {\left (x^{3} e + 14 \, x^{2} e^{2}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 14 \, x^{2} e^{2} + 4 \, x^{2} e^{\left (x + 2\right )}\right )} \log \left (x\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x*exp(1)^2*log(5)+5600*x*exp(1)^2+600
*x^2*exp(1))*log(x)+(800*x^2+800*x)*exp(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(
1)^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1)^2+600*x^2*exp(1))*log(5)+9600*x*e
xp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, algorithm="maxima")

[Out]

400*x^2*e^2*log(5)^2 + 25*x^4 + 200*(2*log(x)^2 - 2*log(x) + 1)*x^2*e^2 - 200*x^2*(2*log(5) + 7)*e^2 + 600*x^3
*e + 4800*x^2*e^2 + 400*x^2*e^(2*x + 2) + 200*(4*x^2*(log(5) + 3)*e^2 + x^3*e + 4*x*e^2 - 4*e^2)*e^x - 800*(x*
e^2 - e^2)*e^x + 200*(x^3*e + 14*x^2*e^2)*log(5) + 200*(x^3*e + 4*x^2*e^2*log(5) + 14*x^2*e^2 + 4*x^2*e^(x + 2
))*log(x) - x

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 146 vs. \(2 (25) = 50\).
time = 0.32, size = 146, normalized size = 5.84 \begin {gather*} {\left (400 \, x^{2} e^{4} \log \left (5\right )^{2} + 400 \, x^{2} e^{4} \log \left (x\right )^{2} + 600 \, x^{3} e^{3} + 3600 \, x^{2} e^{4} + 400 \, x^{2} e^{\left (2 \, x + 4\right )} + {\left (25 \, x^{4} - x\right )} e^{2} + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 12 \, x^{2} e^{2}\right )} e^{\left (x + 2\right )} + 200 \, {\left (x^{3} e^{3} + 12 \, x^{2} e^{4}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e^{3} + 4 \, x^{2} e^{4} \log \left (5\right ) + 12 \, x^{2} e^{4} + 4 \, x^{2} e^{\left (x + 4\right )}\right )} \log \left (x\right )\right )} e^{\left (-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x*exp(1)^2*log(5)+5600*x*exp(1)^2+600
*x^2*exp(1))*log(x)+(800*x^2+800*x)*exp(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(
1)^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1)^2+600*x^2*exp(1))*log(5)+9600*x*e
xp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, algorithm="fricas")

[Out]

(400*x^2*e^4*log(5)^2 + 400*x^2*e^4*log(x)^2 + 600*x^3*e^3 + 3600*x^2*e^4 + 400*x^2*e^(2*x + 4) + (25*x^4 - x)
*e^2 + 200*(x^3*e + 4*x^2*e^2*log(5) + 12*x^2*e^2)*e^(x + 2) + 200*(x^3*e^3 + 12*x^2*e^4)*log(5) + 200*(x^3*e^
3 + 4*x^2*e^4*log(5) + 12*x^2*e^4 + 4*x^2*e^(x + 4))*log(x))*e^(-2)

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (51) = 102\).
time = 0.28, size = 153, normalized size = 6.12 \begin {gather*} 25 x^{4} + x^{3} \cdot \left (200 e \log {\left (5 \right )} + 600 e\right ) + 400 x^{2} e^{2} e^{2 x} + 400 x^{2} e^{2} \log {\left (x \right )}^{2} + x^{2} \cdot \left (400 e^{2} \log {\left (5 \right )}^{2} + 3600 e^{2} + 2400 e^{2} \log {\left (5 \right )}\right ) - x + \left (200 e x^{3} + 800 x^{2} e^{2} \log {\left (5 \right )} + 2400 x^{2} e^{2}\right ) \log {\left (x \right )} + \left (200 e x^{3} + 800 x^{2} e^{2} \log {\left (x \right )} + 800 x^{2} e^{2} \log {\left (5 \right )} + 2400 x^{2} e^{2}\right ) e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(800*x*exp(1)**2*ln(x)**2+((800*x**2+1600*x)*exp(1)**2*exp(x)+1600*x*exp(1)**2*ln(5)+5600*x*exp(1)**2
+600*x**2*exp(1))*ln(x)+(800*x**2+800*x)*exp(1)**2*exp(x)**2+((800*x**2+1600*x)*exp(1)**2*ln(5)+(2400*x**2+560
0*x)*exp(1)**2+(200*x**3+600*x**2)*exp(1))*exp(x)+800*x*exp(1)**2*ln(5)**2+(5600*x*exp(1)**2+600*x**2*exp(1))*
ln(5)+9600*x*exp(1)**2+2000*x**2*exp(1)+100*x**3-1,x)

[Out]

25*x**4 + x**3*(200*E*log(5) + 600*E) + 400*x**2*exp(2)*exp(2*x) + 400*x**2*exp(2)*log(x)**2 + x**2*(400*exp(2
)*log(5)**2 + 3600*exp(2) + 2400*exp(2)*log(5)) - x + (200*E*x**3 + 800*x**2*exp(2)*log(5) + 2400*x**2*exp(2))
*log(x) + (200*E*x**3 + 800*x**2*exp(2)*log(x) + 800*x**2*exp(2)*log(5) + 2400*x**2*exp(2))*exp(x)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (25) = 50\).
time = 0.41, size = 170, normalized size = 6.80 \begin {gather*} 400 \, x^{2} e^{2} \log \left (5\right )^{2} + 25 \, x^{4} + 600 \, x^{3} e + 200 \, x^{3} e^{\left (x + 1\right )} - 400 \, x^{2} e^{2} \log \left (5\right ) + 3400 \, x^{2} e^{2} + 400 \, x^{2} e^{\left (2 \, x + 2\right )} + 200 \, {\left (2 \, x^{2} \log \left (x\right )^{2} - 2 \, x^{2} \log \left (x\right ) + x^{2}\right )} e^{2} + 800 \, {\left (x^{2} \log \left (5\right ) + 3 \, x^{2} + x - 1\right )} e^{\left (x + 2\right )} - 800 \, {\left (x - 1\right )} e^{\left (x + 2\right )} + 200 \, {\left (x^{3} e + 14 \, x^{2} e^{2}\right )} \log \left (5\right ) + 200 \, {\left (x^{3} e + 4 \, x^{2} e^{2} \log \left (5\right ) + 14 \, x^{2} e^{2} + 4 \, x^{2} e^{\left (x + 2\right )}\right )} \log \left (x\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(800*x*exp(1)^2*log(x)^2+((800*x^2+1600*x)*exp(1)^2*exp(x)+1600*x*exp(1)^2*log(5)+5600*x*exp(1)^2+600
*x^2*exp(1))*log(x)+(800*x^2+800*x)*exp(1)^2*exp(x)^2+((800*x^2+1600*x)*exp(1)^2*log(5)+(2400*x^2+5600*x)*exp(
1)^2+(200*x^3+600*x^2)*exp(1))*exp(x)+800*x*exp(1)^2*log(5)^2+(5600*x*exp(1)^2+600*x^2*exp(1))*log(5)+9600*x*e
xp(1)^2+2000*x^2*exp(1)+100*x^3-1,x, algorithm="giac")

[Out]

400*x^2*e^2*log(5)^2 + 25*x^4 + 600*x^3*e + 200*x^3*e^(x + 1) - 400*x^2*e^2*log(5) + 3400*x^2*e^2 + 400*x^2*e^
(2*x + 2) + 200*(2*x^2*log(x)^2 - 2*x^2*log(x) + x^2)*e^2 + 800*(x^2*log(5) + 3*x^2 + x - 1)*e^(x + 2) - 800*(
x - 1)*e^(x + 2) + 200*(x^3*e + 14*x^2*e^2)*log(5) + 200*(x^3*e + 4*x^2*e^2*log(5) + 14*x^2*e^2 + 4*x^2*e^(x +
2))*log(x) - x

________________________________________________________________________________________

Mupad [B]
time = 0.56, size = 110, normalized size = 4.40 \begin {gather*} 200\,x^3\,{\mathrm {e}}^{x+1}-x+400\,x^2\,{\mathrm {e}}^{2\,x+2}+25\,x^4+800\,x^2\,{\mathrm {e}}^{x+2}\,\left (\ln \left (5\right )+3\right )+800\,x^2\,{\mathrm {e}}^{x+2}\,\ln \left (x\right )+200\,x^3\,\mathrm {e}\,\left (\ln \left (5\right )+3\right )+200\,x^3\,\mathrm {e}\,\ln \left (x\right )+400\,x^2\,{\mathrm {e}}^2\,{\left (\ln \left (5\right )+3\right )}^2+400\,x^2\,{\mathrm {e}}^2\,{\ln \left (x\right )}^2+800\,x^2\,{\mathrm {e}}^2\,\ln \left (x\right )\,\left (\ln \left (5\right )+3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)*(exp(2)*(5600*x + 2400*x^2) + exp(1)*(600*x^2 + 200*x^3) + exp(2)*log(5)*(1600*x + 800*x^2)) + log(
5)*(5600*x*exp(2) + 600*x^2*exp(1)) + log(x)*(5600*x*exp(2) + 600*x^2*exp(1) + exp(2)*exp(x)*(1600*x + 800*x^2
) + 1600*x*exp(2)*log(5)) + 9600*x*exp(2) + 2000*x^2*exp(1) + 100*x^3 + 800*x*exp(2)*log(5)^2 + exp(2*x)*exp(2
)*(800*x + 800*x^2) + 800*x*exp(2)*log(x)^2 - 1,x)

[Out]

200*x^3*exp(x + 1) - x + 400*x^2*exp(2*x + 2) + 25*x^4 + 800*x^2*exp(x + 2)*(log(5) + 3) + 800*x^2*exp(x + 2)*
log(x) + 200*x^3*exp(1)*(log(5) + 3) + 200*x^3*exp(1)*log(x) + 400*x^2*exp(2)*(log(5) + 3)^2 + 400*x^2*exp(2)*
log(x)^2 + 800*x^2*exp(2)*log(x)*(log(5) + 3)

________________________________________________________________________________________