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

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

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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 {gather*} -\frac {81 x^8}{390625}+\frac {108 x^7}{15625}+\frac {324 e^{x/24} x^6}{15625}-\frac {54 x^6}{625}-\frac {324}{625} e^{x/24} x^5+\frac {12 x^5}{25}+\frac {108}{25} e^{x/24} x^4-\frac {486}{625} e^{x/12} x^4-x^4-12 e^{x/24} x^3+\frac {324}{25} e^{x/12} x^3-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2-108 e^{x/8} x-81 e^{x/6} \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-10546875 e^{x/6}-3125000 x^3+1875000 x^4-405000 x^5+37800 x^6-1296 x^7+e^{x/8} \left (-84375000+9703125 x+1265625 x^2\right )+e^{x/12} \left (-84375000 x+26859375 x^2-1586250 x^3-50625 x^4\right )+e^{x/24} \left (-28125000 x^2+13109375 x^3-1884375 x^4+80325 x^5+675 x^6\right )\right ) \, dx}{781250}\\ &=-x^4+\frac {12 x^5}{25}-\frac {54 x^6}{625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}+\frac {\int e^{x/8} \left (-84375000+9703125 x+1265625 x^2\right ) \, dx}{781250}+\frac {\int e^{x/12} \left (-84375000 x+26859375 x^2-1586250 x^3-50625 x^4\right ) \, dx}{781250}+\frac {\int e^{x/24} \left (-28125000 x^2+13109375 x^3-1884375 x^4+80325 x^5+675 x^6\right ) \, dx}{781250}-\frac {27}{2} \int e^{x/6} \, dx\\ &=-81 e^{x/6}-x^4+\frac {12 x^5}{25}-\frac {54 x^6}{625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}+\frac {\int \left (-84375000 e^{x/8}+9703125 e^{x/8} x+1265625 e^{x/8} x^2\right ) \, dx}{781250}+\frac {\int \left (-84375000 e^{x/12} x+26859375 e^{x/12} x^2-1586250 e^{x/12} x^3-50625 e^{x/12} x^4\right ) \, dx}{781250}+\frac {\int \left (-28125000 e^{x/24} x^2+13109375 e^{x/24} x^3-1884375 e^{x/24} x^4+80325 e^{x/24} x^5+675 e^{x/24} x^6\right ) \, dx}{781250}\\ &=-81 e^{x/6}-x^4+\frac {12 x^5}{25}-\frac {54 x^6}{625}+\frac {108 x^7}{15625}-\frac {81 x^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} x \, dx+\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} x \, dx\\ &=-864 e^{x/8}-81 e^{x/6}-1296 e^{x/12} x+\frac {2484}{25} e^{x/8} x-864 e^{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 {12 x^5}{25}+\frac {38556 e^{x/24} x^5}{15625}-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^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} x \, dx+\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} x \, dx-\frac {30204}{25} \int e^{x/24} x^2 \, dx+1296 \int e^{x/12} \, dx+1728 \int e^{x/24} x \, dx\\ &=15552 e^{x/12}-\frac {41472 e^{x/8}}{25}-81 e^{x/6}+41472 e^{x/24} x-\frac {279936}{25} e^{x/12} x-108 e^{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 {1106244 e^{x/24} x^4}{3125}-\frac {486}{625} e^{x/12} x^4+\frac {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^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} x \, dx+\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} x \, dx\\ &=-995328 e^{x/24}+\frac {3359232 e^{x/12}}{25}-81 e^{x/6}+\frac {35831808}{25} e^{x/24} x-\frac {20155392}{625} e^{x/12} x-108 e^{x/8} x-\frac {53747712}{125} e^{x/24} x^2-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2+\frac {107457924 e^{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 {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}-\frac {4478976 \int e^{x/24} x^3 \, dx}{3125}+\frac {1679616}{625} \int e^{x/12} x \, dx+\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} x \, dx-\frac {34795008}{25} \int e^{x/24} \, dx\\ &=-\frac {859963392 e^{x/24}}{25}+\frac {241864704 e^{x/12}}{625}-81 e^{x/6}+\frac {2579890176}{125} e^{x/24} x-108 e^{x/8} x-\frac {7739670528 e^{x/24} x^2}{3125}-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2-12 e^{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 {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^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} x \, dx}{3125}-\frac {2400731136}{125} \int e^{x/24} \, dx\\ &=-\frac {61917364224 e^{x/24}}{125}-81 e^{x/6}+\frac {371504185344 e^{x/24} x}{3125}-108 e^{x/8} x-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2-12 e^{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 {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}-\frac {15479341056 \int e^{x/24} x \, dx}{3125}-\frac {307006930944 \int e^{x/24} \, dx}{3125}\\ &=-\frac {8916100448256 e^{x/24}}{3125}-81 e^{x/6}-108 e^{x/8} x-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2-12 e^{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 {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}+\frac {371504185344 \int e^{x/24} \, dx}{3125}\\ &=-81 e^{x/6}-108 e^{x/8} x-54 e^{x/12} x^2+\frac {324}{25} e^{x/8} x^2-12 e^{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 {12 x^5}{25}-\frac {324}{625} e^{x/24} x^5-\frac {54 x^6}{625}+\frac {324 e^{x/24} x^6}{15625}+\frac {108 x^7}{15625}-\frac {81 x^8}{390625}\\ \end {aligned} \end {gather*}

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

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 {gather*} -\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} \, {\left (3 \, x^{2} - 25 \, x\right )} e^{\left (\frac {1}{8} \, x\right )} - \frac {54}{625} \, {\left (9 \, x^{4} - 150 \, x^{3} + 625 \, x^{2}\right )} e^{\left (\frac {1}{12} \, x\right )} + \frac {12}{15625} \, {\left (27 \, x^{6} - 675 \, x^{5} + 5625 \, x^{4} - 15625 \, x^{3}\right )} e^{\left (\frac {1}{24} \, x\right )} - 81 \, e^{\left (\frac {1}{6} \, x\right )} \end {gather*}

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 {gather*} -\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} \, {\left (3 \, x^{2} - 25 \, x\right )} e^{\left (\frac {1}{8} \, x\right )} - \frac {54}{625} \, {\left (9 \, x^{4} - 150 \, x^{3} + 625 \, x^{2}\right )} e^{\left (\frac {1}{12} \, x\right )} + \frac {12}{15625} \, {\left (27 \, x^{6} - 675 \, x^{5} + 5625 \, x^{4} - 15625 \, x^{3}\right )} e^{\left (\frac {1}{24} \, x\right )} - 81 \, e^{\left (\frac {1}{6} \, x\right )} \end {gather*}

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	\(-81 \,{\mathrm e}^{\frac {x}{6}}+\frac {\left (10125000 x^{2}-84375000 x \right ) {\mathrm e}^{\frac {x}{8}}}{781250}+\frac {\left (-607500 x^{4}[phone] x^{3}-42187500 x^{2}\right ) {\mathrm e}^{\frac {x}{12}}}{781250}+\frac {\left (16200 x^{6}-405000 x^{5}+3375000 x^{4}-9375000 x^{3}\right ) {\mathrm e}^{\frac {x}{24}}}{781250}-\frac {81 x^{8}}{390625}+\frac {108 x^{7}}{15625}-\frac {54 x^{6}}{625}+\frac {12 x^{5}}{25}-x^{4}\)	\(97\)
derivativedivides	\(-x^{4}+\frac {12 x^{5}}{25}-\frac {54 x^{6}}{625}+\frac {108 x^{7}}{15625}-\frac {81 x^{8}}{390625}-81 \,{\mathrm e}^{\frac {x}{6}}-108 \,{\mathrm e}^{\frac {x}{8}} x +\frac {324 \,{\mathrm e}^{\frac {x}{8}} x^{2}}{25}-54 \,{\mathrm e}^{\frac {x}{12}} x^{2}+\frac {324 \,{\mathrm e}^{\frac {x}{12}} x^{3}}{25}-\frac {486 \,{\mathrm e}^{\frac {x}{12}} x^{4}}{625}-12 \,{\mathrm e}^{\frac {x}{24}} x^{3}+\frac {108 \,{\mathrm e}^{\frac {x}{24}} x^{4}}{25}-\frac {324 \,{\mathrm e}^{\frac {x}{24}} x^{5}}{625}+\frac {324 \,{\mathrm e}^{\frac {x}{24}} x^{6}}{15625}\)	\(124\)
default	\(-x^{4}+\frac {12 x^{5}}{25}-\frac {54 x^{6}}{625}+\frac {108 x^{7}}{15625}-\frac {81 x^{8}}{390625}-81 \,{\mathrm e}^{\frac {x}{6}}-108 \,{\mathrm e}^{\frac {x}{8}} x +\frac {324 \,{\mathrm e}^{\frac {x}{8}} x^{2}}{25}-54 \,{\mathrm e}^{\frac {x}{12}} x^{2}+\frac {324 \,{\mathrm e}^{\frac {x}{12}} x^{3}}{25}-\frac {486 \,{\mathrm e}^{\frac {x}{12}} x^{4}}{625}-12 \,{\mathrm e}^{\frac {x}{24}} x^{3}+\frac {108 \,{\mathrm e}^{\frac {x}{24}} x^{4}}{25}-\frac {324 \,{\mathrm e}^{\frac {x}{24}} x^{5}}{625}+\frac {324 \,{\mathrm e}^{\frac {x}{24}} x^{6}}{15625}\)	\(124\)

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 {gather*} -\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} \, {\left (3 \, x^{2} - 25 \, x\right )} e^{\left (\frac {1}{8} \, x\right )} - \frac {54}{625} \, {\left (9 \, x^{4} - 150 \, x^{3} + 625 \, x^{2}\right )} e^{\left (\frac {1}{12} \, x\right )} + \frac {12}{15625} \, {\left (27 \, x^{6} - 675 \, x^{5} + 5625 \, x^{4} - 15625 \, x^{3}\right )} e^{\left (\frac {1}{24} \, x\right )} - 81 \, e^{\left (\frac {1}{6} \, x\right )} \end {gather*}

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 {gather*} -\frac {{\left (25\,x+75\,{\mathrm {e}}^{x/24}-3\,x^2\right )}^4}{390625} \end {gather*}

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 {gather*} - \frac {81 x^{8}}{390625} + \frac {108 x^{7}}{15625} - \frac {54 x^{6}}{625} + \frac {12 x^{5}}{25} - x^{4} + \frac {\left (3164062500 x^{2} - 26367187500 x\right ) e^{\frac {x}{8}}}{244140625} + \frac {\left (- 189843750 x^{4} + 3164062500 x^{3} - 13183593750 x^{2}\right ) e^{\frac {x}{12}}}{244140625} + \frac {\left (5062500 x^{6} - 126562500 x^{5} + 1054687500 x^{4} - 2929687500 x^{3}\right ) e^{\frac {x}{24}}}{244140625} - 81 e^{\frac {x}{6}} \end {gather*}

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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