3.63.26 \(\int \frac {-25+256 x+500 e^{4 x} x+1472 x^2+4080 x^3+7220 x^4+8500 x^5+6900 x^6+3500 x^7+1000 x^8+e^{3 x} (1700 x+2500 x^2+1500 x^3)+e^{2 x} (2160 x+6300 x^2+8400 x^3+6000 x^4+1500 x^5)+e^x (1216 x+5280 x^2+10860 x^3+13700 x^4+10200 x^5+4500 x^6+500 x^7)}{125 x} \, dx\)

Optimal. Leaf size=20 \[ \left (\frac {4}{5}+e^x+x+x^2\right )^4-\frac {\log (x)}{5} \]

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Rubi [B]  time = 0.56, antiderivative size = 199, normalized size of antiderivative = 9.95, number of steps used = 61, number of rules used = 5, integrand size = 143, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {12, 14, 2194, 2196, 2176} \begin {gather*} x^8+4 x^7+4 e^x x^6+\frac {46 x^6}{5}+12 e^x x^5+\frac {68 x^5}{5}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {361 x^4}{25}+\frac {116 e^x x^3}{5}+12 e^{2 x} x^3+\frac {272 x^3}{25}+\frac {432 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {736 x^2}{125}+\frac {192 e^x x}{25}+\frac {48}{5} e^{2 x} x+4 e^{3 x} x+\frac {256 x}{125}+\frac {256 e^x}{125}+\frac {96 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}-\frac {\log (x)}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-25 + 256*x + 500*E^(4*x)*x + 1472*x^2 + 4080*x^3 + 7220*x^4 + 8500*x^5 + 6900*x^6 + 3500*x^7 + 1000*x^8
+ E^(3*x)*(1700*x + 2500*x^2 + 1500*x^3) + E^(2*x)*(2160*x + 6300*x^2 + 8400*x^3 + 6000*x^4 + 1500*x^5) + E^x*
(1216*x + 5280*x^2 + 10860*x^3 + 13700*x^4 + 10200*x^5 + 4500*x^6 + 500*x^7))/(125*x),x]

[Out]

(256*E^x)/125 + (96*E^(2*x))/25 + (16*E^(3*x))/5 + E^(4*x) + (256*x)/125 + (192*E^x*x)/25 + (48*E^(2*x)*x)/5 +
4*E^(3*x)*x + (736*x^2)/125 + (432*E^x*x^2)/25 + (78*E^(2*x)*x^2)/5 + 4*E^(3*x)*x^2 + (272*x^3)/25 + (116*E^x
*x^3)/5 + 12*E^(2*x)*x^3 + (361*x^4)/25 + (108*E^x*x^4)/5 + 6*E^(2*x)*x^4 + (68*x^5)/5 + 12*E^x*x^5 + (46*x^6)
/5 + 4*E^x*x^6 + 4*x^7 + x^8 - Log[x]/5

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 2176

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] &&  !$UseGamma === True

Rule 2194

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 2196

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] &&  !$UseGamma === True

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{125} \int \frac {-25+256 x+500 e^{4 x} x+1472 x^2+4080 x^3+7220 x^4+8500 x^5+6900 x^6+3500 x^7+1000 x^8+e^{3 x} \left (1700 x+2500 x^2+1500 x^3\right )+e^{2 x} \left (2160 x+6300 x^2+8400 x^3+6000 x^4+1500 x^5\right )+e^x \left (1216 x+5280 x^2+10860 x^3+13700 x^4+10200 x^5+4500 x^6+500 x^7\right )}{x} \, dx\\ &=\frac {1}{125} \int \left (500 e^{4 x}+60 e^{2 x} \left (4+5 x+5 x^2\right ) \left (9+15 x+5 x^2\right )+4 e^x \left (4+5 x+5 x^2\right )^2 \left (19+35 x+5 x^2\right )+100 e^{3 x} \left (17+25 x+15 x^2\right )+\frac {-25+256 x+1472 x^2+4080 x^3+7220 x^4+8500 x^5+6900 x^6+3500 x^7+1000 x^8}{x}\right ) \, dx\\ &=\frac {1}{125} \int \frac {-25+256 x+1472 x^2+4080 x^3+7220 x^4+8500 x^5+6900 x^6+3500 x^7+1000 x^8}{x} \, dx+\frac {4}{125} \int e^x \left (4+5 x+5 x^2\right )^2 \left (19+35 x+5 x^2\right ) \, dx+\frac {12}{25} \int e^{2 x} \left (4+5 x+5 x^2\right ) \left (9+15 x+5 x^2\right ) \, dx+\frac {4}{5} \int e^{3 x} \left (17+25 x+15 x^2\right ) \, dx+4 \int e^{4 x} \, dx\\ &=e^{4 x}+\frac {1}{125} \int \left (256-\frac {25}{x}+1472 x+4080 x^2+7220 x^3+8500 x^4+6900 x^5+3500 x^6+1000 x^7\right ) \, dx+\frac {4}{125} \int \left (304 e^x+1320 e^x x+2715 e^x x^2+3425 e^x x^3+2550 e^x x^4+1125 e^x x^5+125 e^x x^6\right ) \, dx+\frac {12}{25} \int \left (36 e^{2 x}+105 e^{2 x} x+140 e^{2 x} x^2+100 e^{2 x} x^3+25 e^{2 x} x^4\right ) \, dx+\frac {4}{5} \int \left (17 e^{3 x}+25 e^{3 x} x+15 e^{3 x} x^2\right ) \, dx\\ &=e^{4 x}+\frac {256 x}{125}+\frac {736 x^2}{125}+\frac {272 x^3}{25}+\frac {361 x^4}{25}+\frac {68 x^5}{5}+\frac {46 x^6}{5}+4 x^7+x^8-\frac {\log (x)}{5}+4 \int e^x x^6 \, dx+\frac {1216 \int e^x \, dx}{125}+12 \int e^{3 x} x^2 \, dx+12 \int e^{2 x} x^4 \, dx+\frac {68}{5} \int e^{3 x} \, dx+\frac {432}{25} \int e^{2 x} \, dx+20 \int e^{3 x} x \, dx+36 \int e^x x^5 \, dx+\frac {1056}{25} \int e^x x \, dx+48 \int e^{2 x} x^3 \, dx+\frac {252}{5} \int e^{2 x} x \, dx+\frac {336}{5} \int e^{2 x} x^2 \, dx+\frac {408}{5} \int e^x x^4 \, dx+\frac {2172}{25} \int e^x x^2 \, dx+\frac {548}{5} \int e^x x^3 \, dx\\ &=\frac {1216 e^x}{125}+\frac {216 e^{2 x}}{25}+\frac {68 e^{3 x}}{15}+e^{4 x}+\frac {256 x}{125}+\frac {1056 e^x x}{25}+\frac {126}{5} e^{2 x} x+\frac {20}{3} e^{3 x} x+\frac {736 x^2}{125}+\frac {2172 e^x x^2}{25}+\frac {168}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {548 e^x x^3}{5}+24 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {408 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+36 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}-\frac {20}{3} \int e^{3 x} \, dx-8 \int e^{3 x} x \, dx-24 \int e^{2 x} x^3 \, dx-24 \int e^x x^5 \, dx-\frac {126}{5} \int e^{2 x} \, dx-\frac {1056 \int e^x \, dx}{25}-\frac {336}{5} \int e^{2 x} x \, dx-72 \int e^{2 x} x^2 \, dx-\frac {4344}{25} \int e^x x \, dx-180 \int e^x x^4 \, dx-\frac {1632}{5} \int e^x x^3 \, dx-\frac {1644}{5} \int e^x x^2 \, dx\\ &=-\frac {4064 e^x}{125}-\frac {99 e^{2 x}}{25}+\frac {104 e^{3 x}}{45}+e^{4 x}+\frac {256 x}{125}-\frac {3288 e^x x}{25}-\frac {42}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}-\frac {6048 e^x x^2}{25}-\frac {12}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}-\frac {1084 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}-\frac {492 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}+\frac {8}{3} \int e^{3 x} \, dx+\frac {168}{5} \int e^{2 x} \, dx+36 \int e^{2 x} x^2 \, dx+72 \int e^{2 x} x \, dx+120 \int e^x x^4 \, dx+\frac {4344 \int e^x \, dx}{25}+\frac {3288}{5} \int e^x x \, dx+720 \int e^x x^3 \, dx+\frac {4896}{5} \int e^x x^2 \, dx\\ &=\frac {17656 e^x}{125}+\frac {321 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}+\frac {256 x}{125}+\frac {13152 e^x x}{25}+\frac {138}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}+\frac {18432 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {2516 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}-36 \int e^{2 x} \, dx-36 \int e^{2 x} x \, dx-480 \int e^x x^3 \, dx-\frac {3288 \int e^x \, dx}{5}-\frac {9792}{5} \int e^x x \, dx-2160 \int e^x x^2 \, dx\\ &=-\frac {64544 e^x}{125}-\frac {129 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}+\frac {256 x}{125}-\frac {35808 e^x x}{25}+\frac {48}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}-\frac {35568 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {116 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}+18 \int e^{2 x} \, dx+1440 \int e^x x^2 \, dx+\frac {9792 \int e^x \, dx}{5}+4320 \int e^x x \, dx\\ &=\frac {180256 e^x}{125}+\frac {96 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}+\frac {256 x}{125}+\frac {72192 e^x x}{25}+\frac {48}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}+\frac {432 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {116 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}-2880 \int e^x x \, dx-4320 \int e^x \, dx\\ &=-\frac {359744 e^x}{125}+\frac {96 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}+\frac {256 x}{125}+\frac {192 e^x x}{25}+\frac {48}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}+\frac {432 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {116 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}+2880 \int e^x \, dx\\ &=\frac {256 e^x}{125}+\frac {96 e^{2 x}}{25}+\frac {16 e^{3 x}}{5}+e^{4 x}+\frac {256 x}{125}+\frac {192 e^x x}{25}+\frac {48}{5} e^{2 x} x+4 e^{3 x} x+\frac {736 x^2}{125}+\frac {432 e^x x^2}{25}+\frac {78}{5} e^{2 x} x^2+4 e^{3 x} x^2+\frac {272 x^3}{25}+\frac {116 e^x x^3}{5}+12 e^{2 x} x^3+\frac {361 x^4}{25}+\frac {108 e^x x^4}{5}+6 e^{2 x} x^4+\frac {68 x^5}{5}+12 e^x x^5+\frac {46 x^6}{5}+4 e^x x^6+4 x^7+x^8-\frac {\log (x)}{5}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.10, size = 106, normalized size = 5.30 \begin {gather*} \frac {1}{125} \left (125 e^{4 x}+100 e^{3 x} \left (4+5 x+5 x^2\right )+30 e^{2 x} \left (4+5 x+5 x^2\right )^2+4 e^x \left (4+5 x+5 x^2\right )^3+x \left (256+736 x+1360 x^2+1805 x^3+1700 x^4+1150 x^5+500 x^6+125 x^7\right )-25 \log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-25 + 256*x + 500*E^(4*x)*x + 1472*x^2 + 4080*x^3 + 7220*x^4 + 8500*x^5 + 6900*x^6 + 3500*x^7 + 100
0*x^8 + E^(3*x)*(1700*x + 2500*x^2 + 1500*x^3) + E^(2*x)*(2160*x + 6300*x^2 + 8400*x^3 + 6000*x^4 + 1500*x^5)
+ E^x*(1216*x + 5280*x^2 + 10860*x^3 + 13700*x^4 + 10200*x^5 + 4500*x^6 + 500*x^7))/(125*x),x]

[Out]

(125*E^(4*x) + 100*E^(3*x)*(4 + 5*x + 5*x^2) + 30*E^(2*x)*(4 + 5*x + 5*x^2)^2 + 4*E^x*(4 + 5*x + 5*x^2)^3 + x*
(256 + 736*x + 1360*x^2 + 1805*x^3 + 1700*x^4 + 1150*x^5 + 500*x^6 + 125*x^7) - 25*Log[x])/125

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fricas [B]  time = 0.80, size = 121, normalized size = 6.05 \begin {gather*} x^{8} + 4 \, x^{7} + \frac {46}{5} \, x^{6} + \frac {68}{5} \, x^{5} + \frac {361}{25} \, x^{4} + \frac {272}{25} \, x^{3} + \frac {736}{125} \, x^{2} + \frac {4}{5} \, {\left (5 \, x^{2} + 5 \, x + 4\right )} e^{\left (3 \, x\right )} + \frac {6}{25} \, {\left (25 \, x^{4} + 50 \, x^{3} + 65 \, x^{2} + 40 \, x + 16\right )} e^{\left (2 \, x\right )} + \frac {4}{125} \, {\left (125 \, x^{6} + 375 \, x^{5} + 675 \, x^{4} + 725 \, x^{3} + 540 \, x^{2} + 240 \, x + 64\right )} e^{x} + \frac {256}{125} \, x + e^{\left (4 \, x\right )} - \frac {1}{5} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/125*(500*x*exp(x)^4+(1500*x^3+2500*x^2+1700*x)*exp(x)^3+(1500*x^5+6000*x^4+8400*x^3+6300*x^2+2160*
x)*exp(x)^2+(500*x^7+4500*x^6+10200*x^5+13700*x^4+10860*x^3+5280*x^2+1216*x)*exp(x)+1000*x^8+3500*x^7+6900*x^6
+8500*x^5+7220*x^4+4080*x^3+1472*x^2+256*x-25)/x,x, algorithm="fricas")

[Out]

x^8 + 4*x^7 + 46/5*x^6 + 68/5*x^5 + 361/25*x^4 + 272/25*x^3 + 736/125*x^2 + 4/5*(5*x^2 + 5*x + 4)*e^(3*x) + 6/
25*(25*x^4 + 50*x^3 + 65*x^2 + 40*x + 16)*e^(2*x) + 4/125*(125*x^6 + 375*x^5 + 675*x^4 + 725*x^3 + 540*x^2 + 2
40*x + 64)*e^x + 256/125*x + e^(4*x) - 1/5*log(x)

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giac [B]  time = 0.17, size = 151, normalized size = 7.55 \begin {gather*} x^{8} + 4 \, x^{7} + 4 \, x^{6} e^{x} + \frac {46}{5} \, x^{6} + 12 \, x^{5} e^{x} + \frac {68}{5} \, x^{5} + 6 \, x^{4} e^{\left (2 \, x\right )} + \frac {108}{5} \, x^{4} e^{x} + \frac {361}{25} \, x^{4} + 12 \, x^{3} e^{\left (2 \, x\right )} + \frac {116}{5} \, x^{3} e^{x} + \frac {272}{25} \, x^{3} + 4 \, x^{2} e^{\left (3 \, x\right )} + \frac {78}{5} \, x^{2} e^{\left (2 \, x\right )} + \frac {432}{25} \, x^{2} e^{x} + \frac {736}{125} \, x^{2} + 4 \, x e^{\left (3 \, x\right )} + \frac {48}{5} \, x e^{\left (2 \, x\right )} + \frac {192}{25} \, x e^{x} + \frac {256}{125} \, x + e^{\left (4 \, x\right )} + \frac {16}{5} \, e^{\left (3 \, x\right )} + \frac {96}{25} \, e^{\left (2 \, x\right )} + \frac {256}{125} \, e^{x} - \frac {1}{5} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/125*(500*x*exp(x)^4+(1500*x^3+2500*x^2+1700*x)*exp(x)^3+(1500*x^5+6000*x^4+8400*x^3+6300*x^2+2160*
x)*exp(x)^2+(500*x^7+4500*x^6+10200*x^5+13700*x^4+10860*x^3+5280*x^2+1216*x)*exp(x)+1000*x^8+3500*x^7+6900*x^6
+8500*x^5+7220*x^4+4080*x^3+1472*x^2+256*x-25)/x,x, algorithm="giac")

[Out]

x^8 + 4*x^7 + 4*x^6*e^x + 46/5*x^6 + 12*x^5*e^x + 68/5*x^5 + 6*x^4*e^(2*x) + 108/5*x^4*e^x + 361/25*x^4 + 12*x
^3*e^(2*x) + 116/5*x^3*e^x + 272/25*x^3 + 4*x^2*e^(3*x) + 78/5*x^2*e^(2*x) + 432/25*x^2*e^x + 736/125*x^2 + 4*
x*e^(3*x) + 48/5*x*e^(2*x) + 192/25*x*e^x + 256/125*x + e^(4*x) + 16/5*e^(3*x) + 96/25*e^(2*x) + 256/125*e^x -
1/5*log(x)

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maple [B]  time = 0.06, size = 122, normalized size = 6.10

method	result	size
risch	\(\frac {736 x^{2}}{125}+\frac {256 x}{125}-\frac {\ln \relax (x )}{5}+\frac {272 x^{3}}{25}+\frac {361 x^{4}}{25}+\frac {68 x^{5}}{5}+\frac {46 x^{6}}{5}+4 x^{7}+x^{8}+{\mathrm e}^{4 x}+\frac {\left (500 x^{2}+500 x +400\right ) {\mathrm e}^{3 x}}{125}+\frac {\left (750 x^{4}+1500 x^{3}+1950 x^{2}+1200 x +480\right ) {\mathrm e}^{2 x}}{125}+\frac {\left (500 x^{6}+1500 x^{5}+2700 x^{4}+2900 x^{3}+2160 x^{2}+960 x +256\right ) {\mathrm e}^{x}}{125}\)	\(122\)
default	\(\frac {256 x}{125}+{\mathrm e}^{4 x}+12 x^{5} {\mathrm e}^{x}+\frac {16 \,{\mathrm e}^{3 x}}{5}+\frac {96 \,{\mathrm e}^{2 x}}{25}+4 x^{7}+x^{8}-\frac {\ln \relax (x )}{5}+\frac {361 x^{4}}{25}+\frac {272 x^{3}}{25}+\frac {736 x^{2}}{125}+\frac {256 \,{\mathrm e}^{x}}{125}+\frac {46 x^{6}}{5}+\frac {68 x^{5}}{5}+4 x^{2} {\mathrm e}^{3 x}+12 \,{\mathrm e}^{2 x} x^{3}+\frac {78 \,{\mathrm e}^{2 x} x^{2}}{5}+\frac {48 x \,{\mathrm e}^{2 x}}{5}+4 x^{6} {\mathrm e}^{x}+4 x \,{\mathrm e}^{3 x}+\frac {108 \,{\mathrm e}^{x} x^{4}}{5}+\frac {192 \,{\mathrm e}^{x} x}{25}+\frac {432 \,{\mathrm e}^{x} x^{2}}{25}+\frac {116 \,{\mathrm e}^{x} x^{3}}{5}+6 \,{\mathrm e}^{2 x} x^{4}\)	\(152\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/125*(500*x*exp(x)^4+(1500*x^3+2500*x^2+1700*x)*exp(x)^3+(1500*x^5+6000*x^4+8400*x^3+6300*x^2+2160*x)*exp
(x)^2+(500*x^7+4500*x^6+10200*x^5+13700*x^4+10860*x^3+5280*x^2+1216*x)*exp(x)+1000*x^8+3500*x^7+6900*x^6+8500*
x^5+7220*x^4+4080*x^3+1472*x^2+256*x-25)/x,x,method=_RETURNVERBOSE)

[Out]

736/125*x^2+256/125*x-1/5*ln(x)+272/25*x^3+361/25*x^4+68/5*x^5+46/5*x^6+4*x^7+x^8+exp(4*x)+1/125*(500*x^2+500*
x+400)*exp(3*x)+1/125*(750*x^4+1500*x^3+1950*x^2+1200*x+480)*exp(2*x)+1/125*(500*x^6+1500*x^5+2700*x^4+2900*x^
3+2160*x^2+960*x+256)*exp(x)

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maxima [B]  time = 0.39, size = 279, normalized size = 13.95 \begin {gather*} x^{8} + 4 \, x^{7} + \frac {46}{5} \, x^{6} + \frac {68}{5} \, x^{5} + \frac {361}{25} \, x^{4} + \frac {272}{25} \, x^{3} + \frac {736}{125} \, x^{2} + \frac {4}{9} \, {\left (9 \, x^{2} - 6 \, x + 2\right )} e^{\left (3 \, x\right )} + \frac {20}{9} \, {\left (3 \, x - 1\right )} e^{\left (3 \, x\right )} + 3 \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} + 6 \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} + \frac {84}{5} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} + \frac {63}{5} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right )} e^{x} + 36 \, {\left (x^{5} - 5 \, x^{4} + 20 \, x^{3} - 60 \, x^{2} + 120 \, x - 120\right )} e^{x} + \frac {408}{5} \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} + \frac {548}{5} \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + \frac {2172}{25} \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + \frac {1056}{25} \, {\left (x - 1\right )} e^{x} + \frac {256}{125} \, x + e^{\left (4 \, x\right )} + \frac {68}{15} \, e^{\left (3 \, x\right )} + \frac {216}{25} \, e^{\left (2 \, x\right )} + \frac {1216}{125} \, e^{x} - \frac {1}{5} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/125*(500*x*exp(x)^4+(1500*x^3+2500*x^2+1700*x)*exp(x)^3+(1500*x^5+6000*x^4+8400*x^3+6300*x^2+2160*
x)*exp(x)^2+(500*x^7+4500*x^6+10200*x^5+13700*x^4+10860*x^3+5280*x^2+1216*x)*exp(x)+1000*x^8+3500*x^7+6900*x^6
+8500*x^5+7220*x^4+4080*x^3+1472*x^2+256*x-25)/x,x, algorithm="maxima")

[Out]

x^8 + 4*x^7 + 46/5*x^6 + 68/5*x^5 + 361/25*x^4 + 272/25*x^3 + 736/125*x^2 + 4/9*(9*x^2 - 6*x + 2)*e^(3*x) + 20
/9*(3*x - 1)*e^(3*x) + 3*(2*x^4 - 4*x^3 + 6*x^2 - 6*x + 3)*e^(2*x) + 6*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x) + 84/
5*(2*x^2 - 2*x + 1)*e^(2*x) + 63/5*(2*x - 1)*e^(2*x) + 4*(x^6 - 6*x^5 + 30*x^4 - 120*x^3 + 360*x^2 - 720*x + 7
20)*e^x + 36*(x^5 - 5*x^4 + 20*x^3 - 60*x^2 + 120*x - 120)*e^x + 408/5*(x^4 - 4*x^3 + 12*x^2 - 24*x + 24)*e^x
+ 548/5*(x^3 - 3*x^2 + 6*x - 6)*e^x + 2172/25*(x^2 - 2*x + 2)*e^x + 1056/25*(x - 1)*e^x + 256/125*x + e^(4*x)
+ 68/15*e^(3*x) + 216/25*e^(2*x) + 1216/125*e^x - 1/5*log(x)

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mupad [B]  time = 4.73, size = 151, normalized size = 7.55 \begin {gather*} \frac {256\,x}{125}+\frac {96\,{\mathrm {e}}^{2\,x}}{25}+\frac {16\,{\mathrm {e}}^{3\,x}}{5}+{\mathrm {e}}^{4\,x}+\frac {256\,{\mathrm {e}}^x}{125}-\frac {\ln \relax (x)}{5}+\frac {48\,x\,{\mathrm {e}}^{2\,x}}{5}+4\,x\,{\mathrm {e}}^{3\,x}+\frac {432\,x^2\,{\mathrm {e}}^x}{25}+\frac {116\,x^3\,{\mathrm {e}}^x}{5}+\frac {108\,x^4\,{\mathrm {e}}^x}{5}+12\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+\frac {78\,x^2\,{\mathrm {e}}^{2\,x}}{5}+4\,x^2\,{\mathrm {e}}^{3\,x}+12\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}+\frac {192\,x\,{\mathrm {e}}^x}{25}+\frac {736\,x^2}{125}+\frac {272\,x^3}{25}+\frac {361\,x^4}{25}+\frac {68\,x^5}{5}+\frac {46\,x^6}{5}+4\,x^7+x^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((256*x)/125 + 4*x*exp(4*x) + (exp(3*x)*(1700*x + 2500*x^2 + 1500*x^3))/125 + (exp(2*x)*(2160*x + 6300*x^2
+ 8400*x^3 + 6000*x^4 + 1500*x^5))/125 + (exp(x)*(1216*x + 5280*x^2 + 10860*x^3 + 13700*x^4 + 10200*x^5 + 450
0*x^6 + 500*x^7))/125 + (1472*x^2)/125 + (816*x^3)/25 + (1444*x^4)/25 + 68*x^5 + (276*x^6)/5 + 28*x^7 + 8*x^8
- 1/5)/x,x)

[Out]

(256*x)/125 + (96*exp(2*x))/25 + (16*exp(3*x))/5 + exp(4*x) + (256*exp(x))/125 - log(x)/5 + (48*x*exp(2*x))/5
+ 4*x*exp(3*x) + (432*x^2*exp(x))/25 + (116*x^3*exp(x))/5 + (108*x^4*exp(x))/5 + 12*x^5*exp(x) + 4*x^6*exp(x)
+ (78*x^2*exp(2*x))/5 + 4*x^2*exp(3*x) + 12*x^3*exp(2*x) + 6*x^4*exp(2*x) + (192*x*exp(x))/25 + (736*x^2)/125
+ (272*x^3)/25 + (361*x^4)/25 + (68*x^5)/5 + (46*x^6)/5 + 4*x^7 + x^8

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sympy [B]  time = 0.27, size = 136, normalized size = 6.80 \begin {gather*} x^{8} + 4 x^{7} + \frac {46 x^{6}}{5} + \frac {68 x^{5}}{5} + \frac {361 x^{4}}{25} + \frac {272 x^{3}}{25} + \frac {736 x^{2}}{125} + \frac {256 x}{125} + \frac {\left (62500 x^{2} + 62500 x + 50000\right ) e^{3 x}}{15625} + \frac {\left (93750 x^{4} + 187500 x^{3} + 243750 x^{2} + 150000 x + 60000\right ) e^{2 x}}{15625} + \frac {\left (62500 x^{6} + 187500 x^{5} + 337500 x^{4} + 362500 x^{3} + 270000 x^{2} + 120000 x + 32000\right ) e^{x}}{15625} + e^{4 x} - \frac {\log {\relax (x )}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/125*(500*x*exp(x)**4+(1500*x**3+2500*x**2+1700*x)*exp(x)**3+(1500*x**5+6000*x**4+8400*x**3+6300*x*
*2+2160*x)*exp(x)**2+(500*x**7+4500*x**6+10200*x**5+13700*x**4+10860*x**3+5280*x**2+1216*x)*exp(x)+1000*x**8+3
500*x**7+6900*x**6+8500*x**5+7220*x**4+4080*x**3+1472*x**2+256*x-25)/x,x)

[Out]

x**8 + 4*x**7 + 46*x**6/5 + 68*x**5/5 + 361*x**4/25 + 272*x**3/25 + 736*x**2/125 + 256*x/125 + (62500*x**2 + 6
2500*x + 50000)*exp(3*x)/15625 + (93750*x**4 + 187500*x**3 + 243750*x**2 + 150000*x + 60000)*exp(2*x)/15625 +
(62500*x**6 + 187500*x**5 + 337500*x**4 + 362500*x**3 + 270000*x**2 + 120000*x + 32000)*exp(x)/15625 + exp(4*x
) - log(x)/5

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