3.17.81 $\int \frac{-10546875e^{x/6}-3125000x^3+1875000x^4-405000x^5+37800x^6-1296x^7+e^{x/8}(-84375000+9703125x+1265625x^2)+e^{x/12}(-84375000x+26859375x^2-1586250x^3-50625x^4)+e^{x/24}(-28125000x^2+13109375x^3-1884375x^4+80325x^5+675x^6)}{781250}dx$

Optimal. Leaf size=24 $$3-{(3e^{x/24}+x-\frac{3x^2}{25})}^4$$

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Rubi [B]  time = 0.51, antiderivative size = 161, normalized size of antiderivative = 6.71, number of steps used = 54, number of rules used = 4, integrand size = 118, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.034, Rules used = {12, 2194, 2196, 2176} $$\begin{array}{c}-\frac{81x^8}{390625}+\frac{108x^7}{15625}+\frac{324e^{x/24}{x}^6}{15625}-\frac{54x^6}{625}-\frac{324}{625}{e}^{x/24}{x}^5+\frac{12x^5}{25}+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4-x^4-12e^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2-108e^{x/8}x-81e^{x/6}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-10546875*E^(x/6) - 3125000*x^3 + 1875000*x^4 - 405000*x^5 + 37800*x^6 - 1296*x^7 + E^(x/8)*(-84375000 +
9703125*x + 1265625*x^2) + E^(x/12)*(-84375000*x + 26859375*x^2 - 1586250*x^3 - 50625*x^4) + E^(x/24)*(-281250
00*x^2 + 13109375*x^3 - 1884375*x^4 + 80325*x^5 + 675*x^6))/781250,x]

[Out]

-81*E^(x/6) - 108*E^(x/8)*x - 54*E^(x/12)*x^2 + (324*E^(x/8)*x^2)/25 - 12*E^(x/24)*x^3 + (324*E^(x/12)*x^3)/25
- x^4 + (108*E^(x/24)*x^4)/25 - (486*E^(x/12)*x^4)/625 + (12*x^5)/25 - (324*E^(x/24)*x^5)/625 - (54*x^6)/625
+ (324*E^(x/24)*x^6)/15625 + (108*x^7)/15625 - (81*x^8)/390625

Rule 12

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

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{array}{c}\begin{array}{rl}\text{integral}& =\frac{\int (-10546875e^{x/6}-3125000x^3+1875000x^4-405000x^5+37800x^6-1296x^7+e^{x/8}(-84375000+9703125x+1265625x^2)+e^{x/12}(-84375000x+26859375x^2-1586250x^3-50625x^4)+e^{x/24}(-28125000x^2+13109375x^3-1884375x^4+80325x^5+675x^6))dx}{781250}\\ & =-x^4+\frac{12x^5}{25}-\frac{54x^6}{625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}+\frac{\int e^{x/8}(-84375000+9703125x+1265625x^2)dx}{781250}+\frac{\int e^{x/12}(-84375000x+26859375x^2-1586250x^3-50625x^4)dx}{781250}+\frac{\int e^{x/24}(-28125000x^2+13109375x^3-1884375x^4+80325x^5+675x^6)dx}{781250}-\frac{27}{2}\int e^{x/6}dx\\ & =-81e^{x/6}-x^4+\frac{12x^5}{25}-\frac{54x^6}{625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}+\frac{\int (-84375000e^{x/8}+9703125e^{x/8}x+1265625e^{x/8}{x}^2)dx}{781250}+\frac{\int (-84375000e^{x/12}x+26859375e^{x/12}{x}^2-1586250e^{x/12}{x}^3-50625e^{x/12}{x}^4)dx}{781250}+\frac{\int (-28125000e^{x/24}{x}^2+13109375e^{x/24}{x}^3-1884375e^{x/24}{x}^4+80325e^{x/24}{x}^5+675e^{x/24}{x}^6)dx}{781250}\\ & =-81e^{x/6}-x^4+\frac{12x^5}{25}-\frac{54x^6}{625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}+\frac{27\int e^{x/24}{x}^{6}dx}{31250}-\frac{81\int e^{x/12}{x}^{4}dx}{1250}+\frac{3213\int e^{x/24}{x}^{5}dx}{31250}+\frac{81}{50}\int e^{x/8}{x}^{2}dx-\frac{1269}{625}\int e^{x/12}{x}^{3}dx-\frac{603}{250}\int e^{x/24}{x}^{4}dx+\frac{621}{50}\int e^{x/8}xdx+\frac{839}{50}\int e^{x/24}{x}^{3}dx+\frac{1719}{50}\int e^{x/12}{x}^{2}dx-36\int e^{x/24}{x}^{2}dx-108\int e^{x/8}dx-108\int e^{x/12}xdx\\ & =-864e^{x/8}-81e^{x/6}-1296e^{x/12}x+\frac{2484}{25}{e}^{x/8}x-864e^{x/24}{x}^2+\frac{10314}{25}{e}^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2+\frac{10068}{25}{e}^{x/24}{x}^3-\frac{15228}{625}{e}^{x/12}{x}^3-x^4-\frac{7236}{125}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}+\frac{38556e^{x/24}{x}^5}{15625}-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-\frac{1944\int e^{x/24}{x}^{5}dx}{15625}+\frac{1944}{625}\int e^{x/12}{x}^{3}dx-\frac{38556\int e^{x/24}{x}^{4}dx}{3125}-\frac{648}{25}\int e^{x/8}xdx+\frac{45684}{625}\int e^{x/12}{x}^{2}dx-\frac{2484}{25}\int e^{x/8}dx+\frac{28944}{125}\int e^{x/24}{x}^{3}dx-\frac{20628}{25}\int e^{x/12}xdx-\frac{30204}{25}\int e^{x/24}{x}^{2}dx+1296\int e^{x/12}dx+1728\int e^{x/24}xdx\\ & =15552e^{x/12}-\frac{41472e^{x/8}}{25}-81e^{x/6}+41472e^{x/24}x-\frac{279936}{25}{e}^{x/12}x-108e^{x/8}x-\frac{746496}{25}{e}^{x/24}{x}^2+\frac{806058}{625}{e}^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2+\frac{744996}{125}{e}^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-x^4-\frac{1106244e^{x/24}{x}^4}{3125}-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}+\frac{46656\int e^{x/24}{x}^{4}dx}{3125}-\frac{69984}{625}\int e^{x/12}{x}^{2}dx+\frac{5184}{25}\int e^{x/8}dx+\frac{3701376\int e^{x/24}{x}^{3}dx}{3125}-\frac{1096416}{625}\int e^{x/12}xdx+\frac{247536}{25}\int e^{x/12}dx-\frac{2083968}{125}\int e^{x/24}{x}^{2}dx-41472\int e^{x/24}dx+\frac{1449792}{25}\int e^{x/24}xdx\\ & =-995328e^{x/24}+\frac{3359232e^{x/12}}{25}-81e^{x/6}+\frac{35831808}{25}{e}^{x/24}x-\frac{20155392}{625}{e}^{x/12}x-108e^{x/8}x-\frac{53747712}{125}{e}^{x/24}{x}^2-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2+\frac{107457924e^{x/24}{x}^3}{3125}+\frac{324}{25}{e}^{x/12}{x}^3-x^4+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-\frac{4478976\int e^{x/24}{x}^{3}dx}{3125}+\frac{1679616}{625}\int e^{x/12}xdx+\frac{13156992}{625}\int e^{x/12}dx-\frac{266499072\int e^{x/24}{x}^{2}dx}{3125}+\frac{100030464}{125}\int e^{x/24}xdx-\frac{34795008}{25}\int e^{x/24}dx\\ & =-\frac{859963392e^{x/24}}{25}+\frac{241864704e^{x/12}}{625}-81e^{x/6}+\frac{2579890176}{125}{e}^{x/24}x-108e^{x/8}x-\frac{7739670528e^{x/24}{x}^2}{3125}-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2-12e^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-x^4+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-\frac{20155392}{625}\int e^{x/12}dx+\frac{322486272\int e^{x/24}{x}^{2}dx}{3125}+\frac{12791955456\int e^{x/24}xdx}{3125}-\frac{2400731136}{125}\int e^{x/24}dx\\ & =-\frac{61917364224e^{x/24}}{125}-81e^{x/6}+\frac{371504185344e^{x/24}x}{3125}-108e^{x/8}x-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2-12e^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-x^4+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-\frac{15479341056\int e^{x/24}xdx}{3125}-\frac{307006930944\int e^{x/24}dx}{3125}\\ & =-\frac{8916100448256e^{x/24}}{3125}-81e^{x/6}-108e^{x/8}x-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2-12e^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-x^4+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}+\frac{371504185344\int e^{x/24}dx}{3125}\\ & =-81e^{x/6}-108e^{x/8}x-54e^{x/12}{x}^2+\frac{324}{25}{e}^{x/8}{x}^2-12e^{x/24}{x}^3+\frac{324}{25}{e}^{x/12}{x}^3-x^4+\frac{108}{25}{e}^{x/24}{x}^4-\frac{486}{625}{e}^{x/12}{x}^4+\frac{12x^5}{25}-\frac{324}{625}{e}^{x/24}{x}^5-\frac{54x^6}{625}+\frac{324e^{x/24}{x}^6}{15625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}\end{array}\end{array}$$

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Mathematica [A]  time = 0.03, size = 23, normalized size = 0.96 $$\begin{array}{c}-\frac{{(75e^{x/24}+(25-3x)x)}^4}{390625}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-10546875*E^(x/6) - 3125000*x^3 + 1875000*x^4 - 405000*x^5 + 37800*x^6 - 1296*x^7 + E^(x/8)*(-84375
000 + 9703125*x + 1265625*x^2) + E^(x/12)*(-84375000*x + 26859375*x^2 - 1586250*x^3 - 50625*x^4) + E^(x/24)*(-
28125000*x^2 + 13109375*x^3 - 1884375*x^4 + 80325*x^5 + 675*x^6))/781250,x]

[Out]

-1/390625*(75*E^(x/24) + (25 - 3*x)*x)^4

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fricas [B]  time = 0.65, size = 96, normalized size = 4.00 $$\begin{array}{c}-\frac{81}{390625}{x}^8+\frac{108}{15625}{x}^7-\frac{54}{625}{x}^6+\frac{12}{25}{x}^5-x^4+\frac{108}{25}(3x^2-25x)e^{\left(\frac{1}{8}x\right)}-\frac{54}{625}(9x^4-150x^3+625x^2)e^{\left(\frac{1}{12}x\right)}+\frac{12}{15625}(27x^6-675x^5+5625x^4-15625x^3)e^{\left(\frac{1}{24}x\right)}-81e^{\left(\frac{1}{6}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-27/2*exp(1/24*x)^4+1/781250*(1265625*x^2+9703125*x-84375000)*exp(1/24*x)^3+1/781250*(-50625*x^4-158
6250*x^3+26859375*x^2-84375000*x)*exp(1/24*x)^2+1/781250*(675*x^6+80325*x^5-1884375*x^4+13109375*x^3-28125000*
x^2)*exp(1/24*x)-648/390625*x^7+756/15625*x^6-324/625*x^5+12/5*x^4-4*x^3,x, algorithm="fricas")

[Out]

-81/390625*x^8 + 108/15625*x^7 - 54/625*x^6 + 12/25*x^5 - x^4 + 108/25*(3*x^2 - 25*x)*e^(1/8*x) - 54/625*(9*x^
4 - 150*x^3 + 625*x^2)*e^(1/12*x) + 12/15625*(27*x^6 - 675*x^5 + 5625*x^4 - 15625*x^3)*e^(1/24*x) - 81*e^(1/6*
x)

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giac [B]  time = 1.45, size = 96, normalized size = 4.00 $$\begin{array}{c}-\frac{81}{390625}{x}^8+\frac{108}{15625}{x}^7-\frac{54}{625}{x}^6+\frac{12}{25}{x}^5-x^4+\frac{108}{25}(3x^2-25x)e^{\left(\frac{1}{8}x\right)}-\frac{54}{625}(9x^4-150x^3+625x^2)e^{\left(\frac{1}{12}x\right)}+\frac{12}{15625}(27x^6-675x^5+5625x^4-15625x^3)e^{\left(\frac{1}{24}x\right)}-81e^{\left(\frac{1}{6}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-27/2*exp(1/24*x)^4+1/781250*(1265625*x^2+9703125*x-84375000)*exp(1/24*x)^3+1/781250*(-50625*x^4-158
6250*x^3+26859375*x^2-84375000*x)*exp(1/24*x)^2+1/781250*(675*x^6+80325*x^5-1884375*x^4+13109375*x^3-28125000*
x^2)*exp(1/24*x)-648/390625*x^7+756/15625*x^6-324/625*x^5+12/5*x^4-4*x^3,x, algorithm="giac")

[Out]

-81/390625*x^8 + 108/15625*x^7 - 54/625*x^6 + 12/25*x^5 - x^4 + 108/25*(3*x^2 - 25*x)*e^(1/8*x) - 54/625*(9*x^
4 - 150*x^3 + 625*x^2)*e^(1/12*x) + 12/15625*(27*x^6 - 675*x^5 + 5625*x^4 - 15625*x^3)*e^(1/24*x) - 81*e^(1/6*
x)

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maple [B]  time = 0.09, size = 97, normalized size = 4.04

method	result	size
risch	$-81{\mathrm{e}}^{\frac{x}{6}}+\frac{(10125000x^2-84375000x){\mathrm{e}}^{\frac{x}{8}}}{781250}+\frac{(-607500x^4+10125000x^3-42187500x^2){\mathrm{e}}^{\frac{x}{12}}}{781250}+\frac{(16200x^6-405000x^5+3375000x^4-9375000x^3){\mathrm{e}}^{\frac{x}{24}}}{781250}-\frac{81x^8}{390625}+\frac{108x^7}{15625}-\frac{54x^6}{625}+\frac{12x^5}{25}-x^4$	$97$
derivativedivides	$-x^4+\frac{12x^5}{25}-\frac{54x^6}{625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-81{\mathrm{e}}^{\frac{x}{6}}-108{\mathrm{e}}^{\frac{x}{8}}x+\frac{324{\mathrm{e}}^{\frac{x}{8}}{x}^2}{25}-54{\mathrm{e}}^{\frac{x}{12}}{x}^2+\frac{324{\mathrm{e}}^{\frac{x}{12}}{x}^3}{25}-\frac{486{\mathrm{e}}^{\frac{x}{12}}{x}^4}{625}-12{\mathrm{e}}^{\frac{x}{24}}{x}^3+\frac{108{\mathrm{e}}^{\frac{x}{24}}{x}^4}{25}-\frac{324{\mathrm{e}}^{\frac{x}{24}}{x}^5}{625}+\frac{324{\mathrm{e}}^{\frac{x}{24}}{x}^6}{15625}$	$124$
default	$-x^4+\frac{12x^5}{25}-\frac{54x^6}{625}+\frac{108x^7}{15625}-\frac{81x^8}{390625}-81{\mathrm{e}}^{\frac{x}{6}}-108{\mathrm{e}}^{\frac{x}{8}}x+\frac{324{\mathrm{e}}^{\frac{x}{8}}{x}^2}{25}-54{\mathrm{e}}^{\frac{x}{12}}{x}^2+\frac{324{\mathrm{e}}^{\frac{x}{12}}{x}^3}{25}-\frac{486{\mathrm{e}}^{\frac{x}{12}}{x}^4}{625}-12{\mathrm{e}}^{\frac{x}{24}}{x}^3+\frac{108{\mathrm{e}}^{\frac{x}{24}}{x}^4}{25}-\frac{324{\mathrm{e}}^{\frac{x}{24}}{x}^5}{625}+\frac{324{\mathrm{e}}^{\frac{x}{24}}{x}^6}{15625}$	$124$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-27/2*exp(1/24*x)^4+1/781250*(1265625*x^2+9703125*x-84375000)*exp(1/24*x)^3+1/781250*(-50625*x^4-1586250*x
^3+26859375*x^2-84375000*x)*exp(1/24*x)^2+1/781250*(675*x^6+80325*x^5-1884375*x^4+13109375*x^3-28125000*x^2)*e
xp(1/24*x)-648/390625*x^7+756/15625*x^6-324/625*x^5+12/5*x^4-4*x^3,x,method=_RETURNVERBOSE)

[Out]

-81*exp(1/6*x)+1/781250*(10125000*x^2-84375000*x)*exp(1/8*x)+1/781250*(-607500*x^4+10125000*x^3-42187500*x^2)*
exp(1/12*x)+1/781250*(16200*x^6-405000*x^5+3375000*x^4-9375000*x^3)*exp(1/24*x)-81/390625*x^8+108/15625*x^7-54
/625*x^6+12/25*x^5-x^4

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maxima [B]  time = 0.46, size = 96, normalized size = 4.00 $$\begin{array}{c}-\frac{81}{390625}{x}^8+\frac{108}{15625}{x}^7-\frac{54}{625}{x}^6+\frac{12}{25}{x}^5-x^4+\frac{108}{25}(3x^2-25x)e^{\left(\frac{1}{8}x\right)}-\frac{54}{625}(9x^4-150x^3+625x^2)e^{\left(\frac{1}{12}x\right)}+\frac{12}{15625}(27x^6-675x^5+5625x^4-15625x^3)e^{\left(\frac{1}{24}x\right)}-81e^{\left(\frac{1}{6}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-27/2*exp(1/24*x)^4+1/781250*(1265625*x^2+9703125*x-84375000)*exp(1/24*x)^3+1/781250*(-50625*x^4-158
6250*x^3+26859375*x^2-84375000*x)*exp(1/24*x)^2+1/781250*(675*x^6+80325*x^5-1884375*x^4+13109375*x^3-28125000*
x^2)*exp(1/24*x)-648/390625*x^7+756/15625*x^6-324/625*x^5+12/5*x^4-4*x^3,x, algorithm="maxima")

[Out]

-81/390625*x^8 + 108/15625*x^7 - 54/625*x^6 + 12/25*x^5 - x^4 + 108/25*(3*x^2 - 25*x)*e^(1/8*x) - 54/625*(9*x^
4 - 150*x^3 + 625*x^2)*e^(1/12*x) + 12/15625*(27*x^6 - 675*x^5 + 5625*x^4 - 15625*x^3)*e^(1/24*x) - 81*e^(1/6*
x)

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mupad [B]  time = 1.18, size = 19, normalized size = 0.79 $$\begin{array}{c}-\frac{{(25x+75{\mathrm{e}}^{x/24}-3x^2)}^4}{390625}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x/8)*(9703125*x + 1265625*x^2 - 84375000))/781250 - (27*exp(x/6))/2 + (exp(x/24)*(13109375*x^3 - 2812
5000*x^2 - 1884375*x^4 + 80325*x^5 + 675*x^6))/781250 - (exp(x/12)*(84375000*x - 26859375*x^2 + 1586250*x^3 +
50625*x^4))/781250 - 4*x^3 + (12*x^4)/5 - (324*x^5)/625 + (756*x^6)/15625 - (648*x^7)/390625,x)

[Out]

-(25*x + 75*exp(x/24) - 3*x^2)^4/390625

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sympy [B]  time = 0.26, size = 100, normalized size = 4.17 $$\begin{array}{c}-\frac{81x^8}{390625}+\frac{108x^7}{15625}-\frac{54x^6}{625}+\frac{12x^5}{25}-x^4+\frac{(3164062500x^2-26367187500x)e^{\frac{x}{8}}}{244140625}+\frac{(-189843750x^4+3164062500x^3-13183593750x^2)e^{\frac{x}{12}}}{244140625}+\frac{(5062500x^6-126562500x^5+1054687500x^4-2929687500x^3)e^{\frac{x}{24}}}{244140625}-81e^{\frac{x}{6}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-27/2*exp(1/24*x)**4+1/781250*(1265625*x**2+9703125*x-84375000)*exp(1/24*x)**3+1/781250*(-50625*x**4
-1586250*x**3+26859375*x**2-84375000*x)*exp(1/24*x)**2+1/781250*(675*x**6+80325*x**5-1884375*x**4+13109375*x**
3-28125000*x**2)*exp(1/24*x)-648/390625*x**7+756/15625*x**6-324/625*x**5+12/5*x**4-4*x**3,x)

[Out]

-81*x**8/390625 + 108*x**7/15625 - 54*x**6/625 + 12*x**5/25 - x**4 + (3164062500*x**2 - 26367187500*x)*exp(x/8
)/244140625 + (-189843750*x**4 + 3164062500*x**3 - 13183593750*x**2)*exp(x/12)/244140625 + (5062500*x**6 - 126
562500*x**5 + 1054687500*x**4 - 2929687500*x**3)*exp(x/24)/244140625 - 81*exp(x/6)

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