3.65.20 \(\int (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} (-72-132 x-60 x^2)+e^5 (52+144 x+132 x^2+40 x^3)+(-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} (-10+50 x^2)+e^{15} (40+80 x-200 x^2-200 x^3)+e^{10} (-60-240 x+120 x^2+600 x^3+300 x^4)+e^5 (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5)) \log (x)+(75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} (-300 x^2-400 x^3)+e^{10} (450 x^2+1200 x^3+750 x^4)+e^5 (-300 x^2-1200 x^3-1500 x^4-600 x^5)) \log ^2(x)) \, dx\)

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

________________________________________________________________________________________

Rubi [B]  time = 0.48, antiderivative size = 470, normalized size of antiderivative = 15.67, number of steps used = 25, number of rules used = 5, integrand size = 282, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2356, 2295, 2304, 6, 2305} \begin {gather*} 25 x^7 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)-2 \left (5-12 e^5+6 e^{10}\right ) x^5+12 \left (1-e^5\right )^2 x^5-2 x^5+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)-60 \left (1-e^5\right )^2 x^5 \log (x)-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4+\frac {25}{2} \left (1-e^5\right )^3 x^4+10 e^5 x^4-11 x^4+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)-50 \left (1-e^5\right )^3 x^4 \log (x)+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3+\frac {50}{9} \left (1-e^5\right )^4 x^3-20 e^{10} x^3+44 e^5 x^3-24 x^3+25 \left (1-e^5\right )^4 x^3 \log ^2(x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)-\frac {50}{3} \left (1-e^5\right )^4 x^3 \log (x)+20 \left (1-e^5\right )^3 x^2-66 e^{10} x^2+72 e^5 x^2-26 x^2-40 \left (1-e^5\right )^3 x^2 \log (x)-2 \left (7+5 e^{20}\right ) x+10 \left (1-e^5\right )^4 x-72 e^{10} x+52 e^5 x+\frac {1}{5} e^{15} (10 x+11)^2-10 \left (1-e^5\right )^4 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-14 - 10*E^20 - 52*x - 72*x^2 - 44*x^3 - 10*x^4 + E^15*(44 + 40*x) + E^10*(-72 - 132*x - 60*x^2) + E^5*(52
+ 144*x + 132*x^2 + 40*x^3) + (-10 - 80*x - 130*x^2 + 40*x^3 + 250*x^4 + 200*x^5 + 50*x^6 + E^20*(-10 + 50*x^
2) + E^15*(40 + 80*x - 200*x^2 - 200*x^3) + E^10*(-60 - 240*x + 120*x^2 + 600*x^3 + 300*x^4) + E^5*(40 + 240*x
+ 160*x^2 - 440*x^3 - 600*x^4 - 200*x^5))*Log[x] + (75*x^2 + 75*E^20*x^2 + 400*x^3 + 750*x^4 + 600*x^5 + 175*
x^6 + E^15*(-300*x^2 - 400*x^3) + E^10*(450*x^2 + 1200*x^3 + 750*x^4) + E^5*(-300*x^2 - 1200*x^3 - 1500*x^4 -
600*x^5))*Log[x]^2,x]

[Out]

52*E^5*x - 72*E^10*x + 10*(1 - E^5)^4*x - 2*(7 + 5*E^20)*x - 26*x^2 + 72*E^5*x^2 - 66*E^10*x^2 + 20*(1 - E^5)^
3*x^2 - 24*x^3 + 44*E^5*x^3 - 20*E^10*x^3 + (50*(1 - E^5)^4*x^3)/9 + (10*(1 - E^5)^2*(13 + 10*E^5 - 5*E^10)*x^
3)/9 - 11*x^4 + 10*E^5*x^4 + (25*(1 - E^5)^3*x^4)/2 - (5*(1 - 11*E^5 + 15*E^10 - 5*E^15)*x^4)/2 - 2*x^5 + 12*(
1 - E^5)^2*x^5 - 2*(5 - 12*E^5 + 6*E^10)*x^5 + (E^15*(11 + 10*x)^2)/5 - 10*(1 - E^5)^4*x*Log[x] - 40*(1 - E^5)
^3*x^2*Log[x] - (50*(1 - E^5)^4*x^3*Log[x])/3 - (10*(1 - E^5)^2*(13 + 10*E^5 - 5*E^10)*x^3*Log[x])/3 - 50*(1 -
E^5)^3*x^4*Log[x] + 10*(1 - 11*E^5 + 15*E^10 - 5*E^15)*x^4*Log[x] - 60*(1 - E^5)^2*x^5*Log[x] + 10*(5 - 12*E^
5 + 6*E^10)*x^5*Log[x] + 25*(1 - E^5)^4*x^3*Log[x]^2 + 100*(1 - E^5)^3*x^4*Log[x]^2 + 150*(1 - E^5)^2*x^5*Log[
x]^2 + 100*(1 - E^5)*x^6*Log[x]^2 + 25*x^7*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 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2304

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 2305

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 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-2 \left (7+5 e^{20}\right ) x-26 x^2-24 x^3-11 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+e^5 \int \left (52+144 x+132 x^2+40 x^3\right ) \, dx+e^{10} \int \left (-72-132 x-60 x^2\right ) \, dx+\int \left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x) \, dx+\int \left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x) \, dx\\ &=52 e^5 x-72 e^{10} x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3-11 x^4+10 e^5 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+\int \left (\left (75+75 e^{20}\right ) x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x) \, dx+\int \left (-10 \left (-1+e^5\right )^4 \log (x)+80 \left (-1+e^5\right )^3 x \log (x)+10 \left (-1+e^5\right )^2 \left (-13-10 e^5+5 e^{10}\right ) x^2 \log (x)-40 \left (-1+11 e^5-15 e^{10}+5 e^{15}\right ) x^3 \log (x)+50 \left (5-12 e^5+6 e^{10}\right ) x^4 \log (x)-200 \left (-1+e^5\right ) x^5 \log (x)+50 x^6 \log (x)\right ) \, dx\\ &=52 e^5 x-72 e^{10} x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3-11 x^4+10 e^5 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+50 \int x^6 \log (x) \, dx+\left (200 \left (1-e^5\right )\right ) \int x^5 \log (x) \, dx-\left (80 \left (1-e^5\right )^3\right ) \int x \log (x) \, dx-\left (10 \left (1-e^5\right )^4\right ) \int \log (x) \, dx-\left (10 \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right )\right ) \int x^2 \log (x) \, dx+\left (50 \left (5-12 e^5+6 e^{10}\right )\right ) \int x^4 \log (x) \, dx+\left (40 \left (1-11 e^5+15 e^{10}-5 e^{15}\right )\right ) \int x^3 \log (x) \, dx+\int \left (75 \left (-1+e^5\right )^4 x^2 \log ^2(x)-400 \left (-1+e^5\right )^3 x^3 \log ^2(x)+750 \left (-1+e^5\right )^2 x^4 \log ^2(x)-600 \left (-1+e^5\right ) x^5 \log ^2(x)+175 x^6 \log ^2(x)\right ) \, dx\\ &=52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5-\frac {50}{9} \left (1-e^5\right ) x^6-\frac {50 x^7}{49}+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+\frac {100}{3} \left (1-e^5\right ) x^6 \log (x)+\frac {50}{7} x^7 \log (x)+175 \int x^6 \log ^2(x) \, dx+\left (600 \left (1-e^5\right )\right ) \int x^5 \log ^2(x) \, dx+\left (750 \left (1-e^5\right )^2\right ) \int x^4 \log ^2(x) \, dx+\left (400 \left (1-e^5\right )^3\right ) \int x^3 \log ^2(x) \, dx+\left (75 \left (1-e^5\right )^4\right ) \int x^2 \log ^2(x) \, dx\\ &=52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5-\frac {50}{9} \left (1-e^5\right ) x^6-\frac {50 x^7}{49}+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+\frac {100}{3} \left (1-e^5\right ) x^6 \log (x)+\frac {50}{7} x^7 \log (x)+25 \left (1-e^5\right )^4 x^3 \log ^2(x)+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)+25 x^7 \log ^2(x)-50 \int x^6 \log (x) \, dx-\left (200 \left (1-e^5\right )\right ) \int x^5 \log (x) \, dx-\left (300 \left (1-e^5\right )^2\right ) \int x^4 \log (x) \, dx-\left (200 \left (1-e^5\right )^3\right ) \int x^3 \log (x) \, dx-\left (50 \left (1-e^5\right )^4\right ) \int x^2 \log (x) \, dx\\ &=52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {50}{9} \left (1-e^5\right )^4 x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4+\frac {25}{2} \left (1-e^5\right )^3 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5+12 \left (1-e^5\right )^2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {50}{3} \left (1-e^5\right )^4 x^3 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)-50 \left (1-e^5\right )^3 x^4 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)-60 \left (1-e^5\right )^2 x^5 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+25 \left (1-e^5\right )^4 x^3 \log ^2(x)+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)+25 x^7 \log ^2(x)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.39, size = 351, normalized size = 11.70 \begin {gather*} -4 x+12 e^5 x-12 e^{10} x+4 e^{15} x-6 x^2+12 e^5 x^2-6 e^{10} x^2-4 x^3+4 e^5 x^3-x^4-10 x \log (x)+40 e^5 x \log (x)-60 e^{10} x \log (x)+40 e^{15} x \log (x)-10 e^{20} x \log (x)-40 x^2 \log (x)+120 e^5 x^2 \log (x)-120 e^{10} x^2 \log (x)+40 e^{15} x^2 \log (x)-60 x^3 \log (x)+120 e^5 x^3 \log (x)-60 e^{10} x^3 \log (x)-40 x^4 \log (x)+40 e^5 x^4 \log (x)-10 x^5 \log (x)+25 x^3 \log ^2(x)-100 e^5 x^3 \log ^2(x)+150 e^{10} x^3 \log ^2(x)-100 e^{15} x^3 \log ^2(x)+25 e^{20} x^3 \log ^2(x)+100 x^4 \log ^2(x)-300 e^5 x^4 \log ^2(x)+300 e^{10} x^4 \log ^2(x)-100 e^{15} x^4 \log ^2(x)+150 x^5 \log ^2(x)-300 e^5 x^5 \log ^2(x)+150 e^{10} x^5 \log ^2(x)+100 x^6 \log ^2(x)-100 e^5 x^6 \log ^2(x)+25 x^7 \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-14 - 10*E^20 - 52*x - 72*x^2 - 44*x^3 - 10*x^4 + E^15*(44 + 40*x) + E^10*(-72 - 132*x - 60*x^2) + E
^5*(52 + 144*x + 132*x^2 + 40*x^3) + (-10 - 80*x - 130*x^2 + 40*x^3 + 250*x^4 + 200*x^5 + 50*x^6 + E^20*(-10 +
50*x^2) + E^15*(40 + 80*x - 200*x^2 - 200*x^3) + E^10*(-60 - 240*x + 120*x^2 + 600*x^3 + 300*x^4) + E^5*(40 +
240*x + 160*x^2 - 440*x^3 - 600*x^4 - 200*x^5))*Log[x] + (75*x^2 + 75*E^20*x^2 + 400*x^3 + 750*x^4 + 600*x^5
+ 175*x^6 + E^15*(-300*x^2 - 400*x^3) + E^10*(450*x^2 + 1200*x^3 + 750*x^4) + E^5*(-300*x^2 - 1200*x^3 - 1500*
x^4 - 600*x^5))*Log[x]^2,x]

[Out]

-4*x + 12*E^5*x - 12*E^10*x + 4*E^15*x - 6*x^2 + 12*E^5*x^2 - 6*E^10*x^2 - 4*x^3 + 4*E^5*x^3 - x^4 - 10*x*Log[
x] + 40*E^5*x*Log[x] - 60*E^10*x*Log[x] + 40*E^15*x*Log[x] - 10*E^20*x*Log[x] - 40*x^2*Log[x] + 120*E^5*x^2*Lo
g[x] - 120*E^10*x^2*Log[x] + 40*E^15*x^2*Log[x] - 60*x^3*Log[x] + 120*E^5*x^3*Log[x] - 60*E^10*x^3*Log[x] - 40
*x^4*Log[x] + 40*E^5*x^4*Log[x] - 10*x^5*Log[x] + 25*x^3*Log[x]^2 - 100*E^5*x^3*Log[x]^2 + 150*E^10*x^3*Log[x]
^2 - 100*E^15*x^3*Log[x]^2 + 25*E^20*x^3*Log[x]^2 + 100*x^4*Log[x]^2 - 300*E^5*x^4*Log[x]^2 + 300*E^10*x^4*Log
[x]^2 - 100*E^15*x^4*Log[x]^2 + 150*x^5*Log[x]^2 - 300*E^5*x^5*Log[x]^2 + 150*E^10*x^5*Log[x]^2 + 100*x^6*Log[
x]^2 - 100*E^5*x^6*Log[x]^2 + 25*x^7*Log[x]^2

________________________________________________________________________________________

fricas [B]  time = 0.56, size = 203, normalized size = 6.77 \begin {gather*} -x^{4} - 4 \, x^{3} + 25 \, {\left (x^{7} + 4 \, x^{6} + 6 \, x^{5} + 4 \, x^{4} + x^{3} e^{20} + x^{3} - 4 \, {\left (x^{4} + x^{3}\right )} e^{15} + 6 \, {\left (x^{5} + 2 \, x^{4} + x^{3}\right )} e^{10} - 4 \, {\left (x^{6} + 3 \, x^{5} + 3 \, x^{4} + x^{3}\right )} e^{5}\right )} \log \relax (x)^{2} - 6 \, x^{2} + 4 \, x e^{15} - 6 \, {\left (x^{2} + 2 \, x\right )} e^{10} + 4 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x\right )} e^{5} - 10 \, {\left (x^{5} + 4 \, x^{4} + 6 \, x^{3} + 4 \, x^{2} + x e^{20} - 4 \, {\left (x^{2} + x\right )} e^{15} + 6 \, {\left (x^{3} + 2 \, x^{2} + x\right )} e^{10} - 4 \, {\left (x^{4} + 3 \, x^{3} + 3 \, x^{2} + x\right )} e^{5} + x\right )} \log \relax (x) - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2)*exp(5)^2+(-600*x^5-1500*x^4-
1200*x^3-300*x^2)*exp(5)+175*x^6+600*x^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*
x^2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^4-440*x^3+160*x^2+240*x+40)*
exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)
*exp(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, algorithm="fricas")

[Out]

-x^4 - 4*x^3 + 25*(x^7 + 4*x^6 + 6*x^5 + 4*x^4 + x^3*e^20 + x^3 - 4*(x^4 + x^3)*e^15 + 6*(x^5 + 2*x^4 + x^3)*e
^10 - 4*(x^6 + 3*x^5 + 3*x^4 + x^3)*e^5)*log(x)^2 - 6*x^2 + 4*x*e^15 - 6*(x^2 + 2*x)*e^10 + 4*(x^3 + 3*x^2 + 3
*x)*e^5 - 10*(x^5 + 4*x^4 + 6*x^3 + 4*x^2 + x*e^20 - 4*(x^2 + x)*e^15 + 6*(x^3 + 2*x^2 + x)*e^10 - 4*(x^4 + 3*
x^3 + 3*x^2 + x)*e^5 + x)*log(x) - 4*x

________________________________________________________________________________________

giac [B]  time = 0.17, size = 400, normalized size = 13.33 \begin {gather*} 25 \, x^{7} \log \relax (x)^{2} - 100 \, x^{6} e^{5} \log \relax (x)^{2} + 100 \, x^{6} \log \relax (x)^{2} + 150 \, x^{5} e^{10} \log \relax (x)^{2} - 300 \, x^{5} e^{5} \log \relax (x)^{2} + 150 \, x^{5} \log \relax (x)^{2} - 100 \, x^{4} e^{15} \log \relax (x)^{2} + 300 \, x^{4} e^{10} \log \relax (x)^{2} - 300 \, x^{4} e^{5} \log \relax (x)^{2} - 10 \, x^{5} \log \relax (x) + 40 \, x^{4} e^{5} \log \relax (x) + 100 \, x^{4} \log \relax (x)^{2} + 25 \, x^{3} e^{20} \log \relax (x)^{2} - 100 \, x^{3} e^{15} \log \relax (x)^{2} + 150 \, x^{3} e^{10} \log \relax (x)^{2} - 100 \, x^{3} e^{5} \log \relax (x)^{2} - 10 \, x^{4} e^{5} - 40 \, x^{4} \log \relax (x) - 60 \, x^{3} e^{10} \log \relax (x) + 120 \, x^{3} e^{5} \log \relax (x) + 25 \, x^{3} \log \relax (x)^{2} - x^{4} + 20 \, x^{3} e^{10} - 40 \, x^{3} e^{5} - 60 \, x^{3} \log \relax (x) + 40 \, x^{2} e^{15} \log \relax (x) - 120 \, x^{2} e^{10} \log \relax (x) + 120 \, x^{2} e^{5} \log \relax (x) - 4 \, x^{3} - 20 \, x^{2} e^{15} + 60 \, x^{2} e^{10} - 60 \, x^{2} e^{5} - 40 \, x^{2} \log \relax (x) - 10 \, x e^{20} \log \relax (x) + 40 \, x e^{15} \log \relax (x) - 60 \, x e^{10} \log \relax (x) + 40 \, x e^{5} \log \relax (x) - 6 \, x^{2} + 4 \, {\left (5 \, x^{2} + 11 \, x\right )} e^{15} - 40 \, x e^{15} - 2 \, {\left (10 \, x^{3} + 33 \, x^{2} + 36 \, x\right )} e^{10} + 60 \, x e^{10} + 2 \, {\left (5 \, x^{4} + 22 \, x^{3} + 36 \, x^{2} + 26 \, x\right )} e^{5} - 40 \, x e^{5} - 10 \, x \log \relax (x) - 4 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2)*exp(5)^2+(-600*x^5-1500*x^4-
1200*x^3-300*x^2)*exp(5)+175*x^6+600*x^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*
x^2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^4-440*x^3+160*x^2+240*x+40)*
exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)
*exp(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, algorithm="giac")

[Out]

25*x^7*log(x)^2 - 100*x^6*e^5*log(x)^2 + 100*x^6*log(x)^2 + 150*x^5*e^10*log(x)^2 - 300*x^5*e^5*log(x)^2 + 150
*x^5*log(x)^2 - 100*x^4*e^15*log(x)^2 + 300*x^4*e^10*log(x)^2 - 300*x^4*e^5*log(x)^2 - 10*x^5*log(x) + 40*x^4*
e^5*log(x) + 100*x^4*log(x)^2 + 25*x^3*e^20*log(x)^2 - 100*x^3*e^15*log(x)^2 + 150*x^3*e^10*log(x)^2 - 100*x^3
*e^5*log(x)^2 - 10*x^4*e^5 - 40*x^4*log(x) - 60*x^3*e^10*log(x) + 120*x^3*e^5*log(x) + 25*x^3*log(x)^2 - x^4 +
20*x^3*e^10 - 40*x^3*e^5 - 60*x^3*log(x) + 40*x^2*e^15*log(x) - 120*x^2*e^10*log(x) + 120*x^2*e^5*log(x) - 4*
x^3 - 20*x^2*e^15 + 60*x^2*e^10 - 60*x^2*e^5 - 40*x^2*log(x) - 10*x*e^20*log(x) + 40*x*e^15*log(x) - 60*x*e^10
*log(x) + 40*x*e^5*log(x) - 6*x^2 + 4*(5*x^2 + 11*x)*e^15 - 40*x*e^15 - 2*(10*x^3 + 33*x^2 + 36*x)*e^10 + 60*x
*e^10 + 2*(5*x^4 + 22*x^3 + 36*x^2 + 26*x)*e^5 - 40*x*e^5 - 10*x*log(x) - 4*x

________________________________________________________________________________________

maple [B]  time = 0.11, size = 243, normalized size = 8.10

method	result	size
norman	\(\left (4 \,{\mathrm e}^{5}-4\right ) x^{3}+\left (-6 \,{\mathrm e}^{10}+12 \,{\mathrm e}^{5}-6\right ) x^{2}+\left (4 \,{\mathrm e}^{15}-12 \,{\mathrm e}^{10}+12 \,{\mathrm e}^{5}-4\right ) x +\left (-100 \,{\mathrm e}^{5}+100\right ) x^{6} \ln \relax (x )^{2}+\left (40 \,{\mathrm e}^{5}-40\right ) x^{4} \ln \relax (x )+\left (-60 \,{\mathrm e}^{10}+120 \,{\mathrm e}^{5}-60\right ) x^{3} \ln \relax (x )+\left (150 \,{\mathrm e}^{10}-300 \,{\mathrm e}^{5}+150\right ) x^{5} \ln \relax (x )^{2}+\left (-100 \,{\mathrm e}^{15}+300 \,{\mathrm e}^{10}-300 \,{\mathrm e}^{5}+100\right ) x^{4} \ln \relax (x )^{2}+\left (40 \,{\mathrm e}^{15}-120 \,{\mathrm e}^{10}+120 \,{\mathrm e}^{5}-40\right ) x^{2} \ln \relax (x )+\left (40 \,{\mathrm e}^{15}-60 \,{\mathrm e}^{10}+40 \,{\mathrm e}^{5}-10-10 \,{\mathrm e}^{20}\right ) x \ln \relax (x )+\left (25 \,{\mathrm e}^{20}-100 \,{\mathrm e}^{15}+150 \,{\mathrm e}^{10}-100 \,{\mathrm e}^{5}+25\right ) x^{3} \ln \relax (x )^{2}-x^{4}-10 x^{5} \ln \relax (x )+25 x^{7} \ln \relax (x )^{2}\)	\(243\)
risch	\(-4 x -120 x^{2} {\mathrm e}^{10} \ln \relax (x )-40 x^{2} \ln \relax (x )-12 x \,{\mathrm e}^{10}+25 x^{7} \ln \relax (x )^{2}+40 x \,{\mathrm e}^{5} \ln \relax (x )+120 x^{3} {\mathrm e}^{5} \ln \relax (x )+4 x \,{\mathrm e}^{15}+40 \ln \relax (x ) {\mathrm e}^{15} x +12 x \,{\mathrm e}^{5}-x^{4}-4 x^{3}-6 x^{2}-60 x^{3} \ln \relax (x )+120 x^{2} {\mathrm e}^{5} \ln \relax (x )+100 x^{6} \ln \relax (x )^{2}-10 x^{5} \ln \relax (x )+100 x^{4} \ln \relax (x )^{2}+12 x^{2} {\mathrm e}^{5}-40 x^{4} \ln \relax (x )-10 x \ln \relax (x )+4 x^{3} {\mathrm e}^{5}-6 \,{\mathrm e}^{10} x^{2}+150 x^{5} \ln \relax (x )^{2}+25 x^{3} \ln \relax (x )^{2}+25 \,{\mathrm e}^{20} x^{3} \ln \relax (x )^{2}-10 \,{\mathrm e}^{20} \ln \relax (x ) x +40 \ln \relax (x ) x^{2} {\mathrm e}^{15}-100 \,{\mathrm e}^{5} \ln \relax (x )^{2} x^{3}-100 \,{\mathrm e}^{15} x^{4} \ln \relax (x )^{2}+150 \,{\mathrm e}^{10} x^{5} \ln \relax (x )^{2}-100 x^{3} \ln \relax (x )^{2} {\mathrm e}^{15}+300 x^{4} \ln \relax (x )^{2} {\mathrm e}^{10}+150 x^{3} \ln \relax (x )^{2} {\mathrm e}^{10}-60 \,{\mathrm e}^{10} \ln \relax (x ) x -300 x^{5} \ln \relax (x )^{2} {\mathrm e}^{5}-100 \,{\mathrm e}^{5} x^{6} \ln \relax (x )^{2}-300 x^{4} \ln \relax (x )^{2} {\mathrm e}^{5}+40 \,{\mathrm e}^{5} x^{4} \ln \relax (x )-60 x^{3} {\mathrm e}^{10} \ln \relax (x )\)	\(326\)
default	\(-4 x -120 x^{2} {\mathrm e}^{10} \ln \relax (x )-40 x^{2} \ln \relax (x )+60 x \,{\mathrm e}^{10}+25 x^{7} \ln \relax (x )^{2}+40 x \,{\mathrm e}^{5} \ln \relax (x )+120 x^{3} {\mathrm e}^{5} \ln \relax (x )-40 x \,{\mathrm e}^{15}+40 \ln \relax (x ) {\mathrm e}^{15} x -40 x \,{\mathrm e}^{5}-x^{4}-4 x^{3}-6 x^{2}-60 x^{3} \ln \relax (x )+120 x^{2} {\mathrm e}^{5} \ln \relax (x )+100 x^{6} \ln \relax (x )^{2}-10 x^{5} \ln \relax (x )+100 x^{4} \ln \relax (x )^{2}-60 x^{2} {\mathrm e}^{5}-40 x^{4} \ln \relax (x )-10 x^{4} {\mathrm e}^{5}-10 x \ln \relax (x )-40 x^{3} {\mathrm e}^{5}+60 \,{\mathrm e}^{10} x^{2}-20 x^{2} {\mathrm e}^{15}+20 x^{3} {\mathrm e}^{10}+150 x^{5} \ln \relax (x )^{2}+25 x^{3} \ln \relax (x )^{2}+25 \,{\mathrm e}^{20} x^{3} \ln \relax (x )^{2}-10 \,{\mathrm e}^{20} \ln \relax (x ) x +40 \ln \relax (x ) x^{2} {\mathrm e}^{15}-100 \,{\mathrm e}^{5} \ln \relax (x )^{2} x^{3}-100 \,{\mathrm e}^{15} x^{4} \ln \relax (x )^{2}+150 \,{\mathrm e}^{10} x^{5} \ln \relax (x )^{2}-100 x^{3} \ln \relax (x )^{2} {\mathrm e}^{15}+300 x^{4} \ln \relax (x )^{2} {\mathrm e}^{10}+150 x^{3} \ln \relax (x )^{2} {\mathrm e}^{10}-60 \,{\mathrm e}^{10} \ln \relax (x ) x +{\mathrm e}^{5} \left (10 x^{4}+44 x^{3}+72 x^{2}+52 x \right )-300 x^{5} \ln \relax (x )^{2} {\mathrm e}^{5}-100 \,{\mathrm e}^{5} x^{6} \ln \relax (x )^{2}-300 x^{4} \ln \relax (x )^{2} {\mathrm e}^{5}+40 \,{\mathrm e}^{5} x^{4} \ln \relax (x )+{\mathrm e}^{15} \left (20 x^{2}+44 x \right )+{\mathrm e}^{10} \left (-20 x^{3}-66 x^{2}-72 x \right )-60 x^{3} {\mathrm e}^{10} \ln \relax (x )\)	\(436\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2)*exp(5)^2+(-600*x^5-1500*x^4-1200*x
^3-300*x^2)*exp(5)+175*x^6+600*x^5+750*x^4+400*x^3+75*x^2)*ln(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*x^2+80*
x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^4-440*x^3+160*x^2+240*x+40)*exp(5)+
50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-80*x-10)*ln(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)*exp(5)^
2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x,method=_RETURNVERBOSE)

[Out]

(4*exp(5)-4)*x^3+(-6*exp(5)^2+12*exp(5)-6)*x^2+(4*exp(5)^3-12*exp(5)^2+12*exp(5)-4)*x+(-100*exp(5)+100)*x^6*ln
(x)^2+(40*exp(5)-40)*x^4*ln(x)+(-60*exp(5)^2+120*exp(5)-60)*x^3*ln(x)+(150*exp(5)^2-300*exp(5)+150)*x^5*ln(x)^
2+(-100*exp(5)^3+300*exp(5)^2-300*exp(5)+100)*x^4*ln(x)^2+(40*exp(5)^3-120*exp(5)^2+120*exp(5)-40)*x^2*ln(x)+(
40*exp(5)^3-60*exp(5)^2+40*exp(5)-10-10*exp(5)^4)*x*ln(x)+(25*exp(5)^4-100*exp(5)^3+150*exp(5)^2-100*exp(5)+25
)*x^3*ln(x)^2-x^4-10*x^5*ln(x)+25*x^7*ln(x)^2

________________________________________________________________________________________

maxima [B]  time = 0.38, size = 526, normalized size = 17.53 \begin {gather*} \frac {25}{49} \, {\left (49 \, \log \relax (x)^{2} - 14 \, \log \relax (x) + 2\right )} x^{7} - \frac {50}{9} \, {\left (18 \, {\left (e^{5} - 1\right )} \log \relax (x)^{2} - 6 \, {\left (e^{5} - 1\right )} \log \relax (x) + e^{5} - 1\right )} x^{6} - \frac {50}{49} \, x^{7} + \frac {50}{9} \, x^{6} {\left (e^{5} - 1\right )} + 6 \, {\left (25 \, {\left (e^{10} - 2 \, e^{5} + 1\right )} \log \relax (x)^{2} - 10 \, {\left (e^{10} - 2 \, e^{5} + 1\right )} \log \relax (x) + 2 \, e^{10} - 4 \, e^{5} + 2\right )} x^{5} - 2 \, x^{5} {\left (6 \, e^{10} - 12 \, e^{5} + 5\right )} - \frac {25}{2} \, {\left (8 \, {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} \log \relax (x)^{2} - 4 \, {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} \log \relax (x) + e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} x^{4} - 2 \, x^{5} + \frac {5}{2} \, x^{4} {\left (5 \, e^{15} - 15 \, e^{10} + 11 \, e^{5} - 1\right )} + \frac {25}{9} \, {\left (9 \, {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} \log \relax (x)^{2} - 6 \, {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} \log \relax (x) + 2 \, e^{20} - 8 \, e^{15} + 12 \, e^{10} - 8 \, e^{5} + 2\right )} x^{3} - 11 \, x^{4} - \frac {10}{9} \, x^{3} {\left (5 \, e^{20} - 20 \, e^{15} + 12 \, e^{10} + 16 \, e^{5} - 13\right )} - 24 \, x^{3} - 20 \, x^{2} {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} - 26 \, x^{2} + 10 \, x {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} - 10 \, x e^{20} + 4 \, {\left (5 \, x^{2} + 11 \, x\right )} e^{15} - 2 \, {\left (10 \, x^{3} + 33 \, x^{2} + 36 \, x\right )} e^{10} + 2 \, {\left (5 \, x^{4} + 22 \, x^{3} + 36 \, x^{2} + 26 \, x\right )} e^{5} + \frac {10}{21} \, {\left (15 \, x^{7} + 70 \, x^{6} + 105 \, x^{5} + 21 \, x^{4} - 91 \, x^{3} - 84 \, x^{2} + 7 \, {\left (5 \, x^{3} - 3 \, x\right )} e^{20} - 7 \, {\left (15 \, x^{4} + 20 \, x^{3} - 12 \, x^{2} - 12 \, x\right )} e^{15} + 21 \, {\left (6 \, x^{5} + 15 \, x^{4} + 4 \, x^{3} - 12 \, x^{2} - 6 \, x\right )} e^{10} - 7 \, {\left (10 \, x^{6} + 36 \, x^{5} + 33 \, x^{4} - 16 \, x^{3} - 36 \, x^{2} - 12 \, x\right )} e^{5} - 21 \, x\right )} \log \relax (x) - 14 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((75*x^2*exp(5)^4+(-400*x^3-300*x^2)*exp(5)^3+(750*x^4+1200*x^3+450*x^2)*exp(5)^2+(-600*x^5-1500*x^4-
1200*x^3-300*x^2)*exp(5)+175*x^6+600*x^5+750*x^4+400*x^3+75*x^2)*log(x)^2+((50*x^2-10)*exp(5)^4+(-200*x^3-200*
x^2+80*x+40)*exp(5)^3+(300*x^4+600*x^3+120*x^2-240*x-60)*exp(5)^2+(-200*x^5-600*x^4-440*x^3+160*x^2+240*x+40)*
exp(5)+50*x^6+200*x^5+250*x^4+40*x^3-130*x^2-80*x-10)*log(x)-10*exp(5)^4+(40*x+44)*exp(5)^3+(-60*x^2-132*x-72)
*exp(5)^2+(40*x^3+132*x^2+144*x+52)*exp(5)-10*x^4-44*x^3-72*x^2-52*x-14,x, algorithm="maxima")

[Out]

25/49*(49*log(x)^2 - 14*log(x) + 2)*x^7 - 50/9*(18*(e^5 - 1)*log(x)^2 - 6*(e^5 - 1)*log(x) + e^5 - 1)*x^6 - 50
/49*x^7 + 50/9*x^6*(e^5 - 1) + 6*(25*(e^10 - 2*e^5 + 1)*log(x)^2 - 10*(e^10 - 2*e^5 + 1)*log(x) + 2*e^10 - 4*e
^5 + 2)*x^5 - 2*x^5*(6*e^10 - 12*e^5 + 5) - 25/2*(8*(e^15 - 3*e^10 + 3*e^5 - 1)*log(x)^2 - 4*(e^15 - 3*e^10 +
3*e^5 - 1)*log(x) + e^15 - 3*e^10 + 3*e^5 - 1)*x^4 - 2*x^5 + 5/2*x^4*(5*e^15 - 15*e^10 + 11*e^5 - 1) + 25/9*(9
*(e^20 - 4*e^15 + 6*e^10 - 4*e^5 + 1)*log(x)^2 - 6*(e^20 - 4*e^15 + 6*e^10 - 4*e^5 + 1)*log(x) + 2*e^20 - 8*e^
15 + 12*e^10 - 8*e^5 + 2)*x^3 - 11*x^4 - 10/9*x^3*(5*e^20 - 20*e^15 + 12*e^10 + 16*e^5 - 13) - 24*x^3 - 20*x^2
*(e^15 - 3*e^10 + 3*e^5 - 1) - 26*x^2 + 10*x*(e^20 - 4*e^15 + 6*e^10 - 4*e^5 + 1) - 10*x*e^20 + 4*(5*x^2 + 11*
x)*e^15 - 2*(10*x^3 + 33*x^2 + 36*x)*e^10 + 2*(5*x^4 + 22*x^3 + 36*x^2 + 26*x)*e^5 + 10/21*(15*x^7 + 70*x^6 +
105*x^5 + 21*x^4 - 91*x^3 - 84*x^2 + 7*(5*x^3 - 3*x)*e^20 - 7*(15*x^4 + 20*x^3 - 12*x^2 - 12*x)*e^15 + 21*(6*x
^5 + 15*x^4 + 4*x^3 - 12*x^2 - 6*x)*e^10 - 7*(10*x^6 + 36*x^5 + 33*x^4 - 16*x^3 - 36*x^2 - 12*x)*e^5 - 21*x)*l
og(x) - 14*x

________________________________________________________________________________________

mupad [B]  time = 4.62, size = 153, normalized size = 5.10 \begin {gather*} x\,\left (4\,{\left ({\mathrm {e}}^5-1\right )}^3-10\,\ln \relax (x)\,{\left ({\mathrm {e}}^5-1\right )}^4\right )+25\,x^7\,{\ln \relax (x)}^2-x^2\,\left (6\,{\left ({\mathrm {e}}^5-1\right )}^2-40\,\ln \relax (x)\,{\left ({\mathrm {e}}^5-1\right )}^3\right )+x^3\,\left (25\,{\left ({\mathrm {e}}^5-1\right )}^4\,{\ln \relax (x)}^2-60\,{\left ({\mathrm {e}}^5-1\right )}^2\,\ln \relax (x)+4\,{\mathrm {e}}^5-4\right )-x^5\,\left (10\,\ln \relax (x)-150\,{\ln \relax (x)}^2\,{\left ({\mathrm {e}}^5-1\right )}^2\right )-x^4\,\left (100\,{\left ({\mathrm {e}}^5-1\right )}^3\,{\ln \relax (x)}^2+\left (40-40\,{\mathrm {e}}^5\right )\,\ln \relax (x)+1\right )-x^6\,{\ln \relax (x)}^2\,\left (100\,{\mathrm {e}}^5-100\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x)^2*(75*x^2*exp(20) - exp(15)*(300*x^2 + 400*x^3) + exp(10)*(450*x^2 + 1200*x^3 + 750*x^4) + 75*x^2 +
400*x^3 + 750*x^4 + 600*x^5 + 175*x^6 - exp(5)*(300*x^2 + 1200*x^3 + 1500*x^4 + 600*x^5)) - 10*exp(20) - 52*x
- exp(10)*(132*x + 60*x^2 + 72) + exp(5)*(144*x + 132*x^2 + 40*x^3 + 52) + log(x)*(exp(20)*(50*x^2 - 10) - 80
*x + exp(15)*(80*x - 200*x^2 - 200*x^3 + 40) + exp(10)*(120*x^2 - 240*x + 600*x^3 + 300*x^4 - 60) + exp(5)*(24
0*x + 160*x^2 - 440*x^3 - 600*x^4 - 200*x^5 + 40) - 130*x^2 + 40*x^3 + 250*x^4 + 200*x^5 + 50*x^6 - 10) - 72*x
^2 - 44*x^3 - 10*x^4 + exp(15)*(40*x + 44) - 14,x)

[Out]

x*(4*(exp(5) - 1)^3 - 10*log(x)*(exp(5) - 1)^4) + 25*x^7*log(x)^2 - x^2*(6*(exp(5) - 1)^2 - 40*log(x)*(exp(5)
- 1)^3) + x^3*(4*exp(5) - 60*log(x)*(exp(5) - 1)^2 + 25*log(x)^2*(exp(5) - 1)^4 - 4) - x^5*(10*log(x) - 150*lo
g(x)^2*(exp(5) - 1)^2) - x^4*(100*log(x)^2*(exp(5) - 1)^3 - log(x)*(40*exp(5) - 40) + 1) - x^6*log(x)^2*(100*e
xp(5) - 100)

________________________________________________________________________________________

sympy [B]  time = 0.45, size = 267, normalized size = 8.90 \begin {gather*} - x^{4} + x^{3} \left (-4 + 4 e^{5}\right ) + x^{2} \left (- 6 e^{10} - 6 + 12 e^{5}\right ) + x \left (- 12 e^{10} - 4 + 12 e^{5} + 4 e^{15}\right ) + \left (- 10 x^{5} - 40 x^{4} + 40 x^{4} e^{5} - 60 x^{3} e^{10} - 60 x^{3} + 120 x^{3} e^{5} - 120 x^{2} e^{10} - 40 x^{2} + 120 x^{2} e^{5} + 40 x^{2} e^{15} - 10 x e^{20} - 60 x e^{10} - 10 x + 40 x e^{5} + 40 x e^{15}\right ) \log {\relax (x )} + \left (25 x^{7} - 100 x^{6} e^{5} + 100 x^{6} - 300 x^{5} e^{5} + 150 x^{5} + 150 x^{5} e^{10} - 100 x^{4} e^{15} - 300 x^{4} e^{5} + 100 x^{4} + 300 x^{4} e^{10} - 100 x^{3} e^{15} - 100 x^{3} e^{5} + 25 x^{3} + 150 x^{3} e^{10} + 25 x^{3} e^{20}\right ) \log {\relax (x )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((75*x**2*exp(5)**4+(-400*x**3-300*x**2)*exp(5)**3+(750*x**4+1200*x**3+450*x**2)*exp(5)**2+(-600*x**5
-1500*x**4-1200*x**3-300*x**2)*exp(5)+175*x**6+600*x**5+750*x**4+400*x**3+75*x**2)*ln(x)**2+((50*x**2-10)*exp(
5)**4+(-200*x**3-200*x**2+80*x+40)*exp(5)**3+(300*x**4+600*x**3+120*x**2-240*x-60)*exp(5)**2+(-200*x**5-600*x*
*4-440*x**3+160*x**2+240*x+40)*exp(5)+50*x**6+200*x**5+250*x**4+40*x**3-130*x**2-80*x-10)*ln(x)-10*exp(5)**4+(
40*x+44)*exp(5)**3+(-60*x**2-132*x-72)*exp(5)**2+(40*x**3+132*x**2+144*x+52)*exp(5)-10*x**4-44*x**3-72*x**2-52
*x-14,x)

[Out]

-x**4 + x**3*(-4 + 4*exp(5)) + x**2*(-6*exp(10) - 6 + 12*exp(5)) + x*(-12*exp(10) - 4 + 12*exp(5) + 4*exp(15))
+ (-10*x**5 - 40*x**4 + 40*x**4*exp(5) - 60*x**3*exp(10) - 60*x**3 + 120*x**3*exp(5) - 120*x**2*exp(10) - 40*
x**2 + 120*x**2*exp(5) + 40*x**2*exp(15) - 10*x*exp(20) - 60*x*exp(10) - 10*x + 40*x*exp(5) + 40*x*exp(15))*lo
g(x) + (25*x**7 - 100*x**6*exp(5) + 100*x**6 - 300*x**5*exp(5) + 150*x**5 + 150*x**5*exp(10) - 100*x**4*exp(15
) - 300*x**4*exp(5) + 100*x**4 + 300*x**4*exp(10) - 100*x**3*exp(15) - 100*x**3*exp(5) + 25*x**3 + 150*x**3*ex
p(10) + 25*x**3*exp(20))*log(x)**2

________________________________________________________________________________________