3.50.47 \(\int \frac {1}{2} (-2 e^x+12 x^2+60 x^3+100 x^4+52 x^5+(9 x+60 x^2+142 x^3+116 x^4+25 x^5) \log (x)+(9 x+45 x^2+72 x^3+43 x^4+3 x^5) \log ^2(x)+(9 x^2+18 x^3+5 x^4) \log ^3(x)+2 x^3 \log ^4(x)) \, dx\) [4947]

Optimal. Leaf size=34 \[ -e^x+\frac {1}{4} x^2 (-x+(-3+x (-4-\log (x))) (x+\log (x)))^2 \]

[Out]

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

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(142\) vs. \(2(34)=68\).
time = 0.44, antiderivative size = 142, normalized size of antiderivative = 4.18, number of steps used = 38, number of rules used = 6, integrand size = 116, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {12, 2225, 2403, 2341, 2342, 1608} \begin {gather*} 4 x^6+\frac {1}{4} x^6 \log ^2(x)+2 x^6 \log (x)+8 x^5+\frac {1}{2} x^5 \log ^3(x)+4 x^5 \log ^2(x)+10 x^5 \log (x)+4 x^4+\frac {1}{4} x^4 \log ^4(x)+2 x^4 \log ^3(x)+\frac {15}{2} x^4 \log ^2(x)+14 x^4 \log (x)+\frac {3}{2} x^3 \log ^3(x)+6 x^3 \log ^2(x)+6 x^3 \log (x)+\frac {9}{4} x^2 \log ^2(x)-e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*E^x + 12*x^2 + 60*x^3 + 100*x^4 + 52*x^5 + (9*x + 60*x^2 + 142*x^3 + 116*x^4 + 25*x^5)*Log[x] + (9*x +
45*x^2 + 72*x^3 + 43*x^4 + 3*x^5)*Log[x]^2 + (9*x^2 + 18*x^3 + 5*x^4)*Log[x]^3 + 2*x^3*Log[x]^4)/2,x]

[Out]

-E^x + 4*x^4 + 8*x^5 + 4*x^6 + 6*x^3*Log[x] + 14*x^4*Log[x] + 10*x^5*Log[x] + 2*x^6*Log[x] + (9*x^2*Log[x]^2)/
4 + 6*x^3*Log[x]^2 + (15*x^4*Log[x]^2)/2 + 4*x^5*Log[x]^2 + (x^6*Log[x]^2)/4 + (3*x^3*Log[x]^3)/2 + 2*x^4*Log[
x]^3 + (x^5*Log[x]^3)/2 + (x^4*Log[x]^4)/4

Rule 12

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

Rule 1608

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

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 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 2403

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} &=\frac {1}{2} \int \left (-2 e^x+12 x^2+60 x^3+100 x^4+52 x^5+\left (9 x+60 x^2+142 x^3+116 x^4+25 x^5\right ) \log (x)+\left (9 x+45 x^2+72 x^3+43 x^4+3 x^5\right ) \log ^2(x)+\left (9 x^2+18 x^3+5 x^4\right ) \log ^3(x)+2 x^3 \log ^4(x)\right ) \, dx\\ &=2 x^3+\frac {15 x^4}{2}+10 x^5+\frac {13 x^6}{3}+\frac {1}{2} \int \left (9 x+60 x^2+142 x^3+116 x^4+25 x^5\right ) \log (x) \, dx+\frac {1}{2} \int \left (9 x+45 x^2+72 x^3+43 x^4+3 x^5\right ) \log ^2(x) \, dx+\frac {1}{2} \int \left (9 x^2+18 x^3+5 x^4\right ) \log ^3(x) \, dx-\int e^x \, dx+\int x^3 \log ^4(x) \, dx\\ &=-e^x+2 x^3+\frac {15 x^4}{2}+10 x^5+\frac {13 x^6}{3}+\frac {1}{4} x^4 \log ^4(x)+\frac {1}{2} \int x^2 \left (9+18 x+5 x^2\right ) \log ^3(x) \, dx+\frac {1}{2} \int \left (9 x \log (x)+60 x^2 \log (x)+142 x^3 \log (x)+116 x^4 \log (x)+25 x^5 \log (x)\right ) \, dx+\frac {1}{2} \int \left (9 x \log ^2(x)+45 x^2 \log ^2(x)+72 x^3 \log ^2(x)+43 x^4 \log ^2(x)+3 x^5 \log ^2(x)\right ) \, dx-\int x^3 \log ^3(x) \, dx\\ &=-e^x+2 x^3+\frac {15 x^4}{2}+10 x^5+\frac {13 x^6}{3}-\frac {1}{4} x^4 \log ^3(x)+\frac {1}{4} x^4 \log ^4(x)+\frac {1}{2} \int \left (9 x^2 \log ^3(x)+18 x^3 \log ^3(x)+5 x^4 \log ^3(x)\right ) \, dx+\frac {3}{4} \int x^3 \log ^2(x) \, dx+\frac {3}{2} \int x^5 \log ^2(x) \, dx+\frac {9}{2} \int x \log (x) \, dx+\frac {9}{2} \int x \log ^2(x) \, dx+\frac {25}{2} \int x^5 \log (x) \, dx+\frac {43}{2} \int x^4 \log ^2(x) \, dx+\frac {45}{2} \int x^2 \log ^2(x) \, dx+30 \int x^2 \log (x) \, dx+36 \int x^3 \log ^2(x) \, dx+58 \int x^4 \log (x) \, dx+71 \int x^3 \log (x) \, dx\\ &=-e^x-\frac {9 x^2}{8}-\frac {4 x^3}{3}+\frac {49 x^4}{16}+\frac {192 x^5}{25}+\frac {287 x^6}{72}+\frac {9}{4} x^2 \log (x)+10 x^3 \log (x)+\frac {71}{4} x^4 \log (x)+\frac {58}{5} x^5 \log (x)+\frac {25}{12} x^6 \log (x)+\frac {9}{4} x^2 \log ^2(x)+\frac {15}{2} x^3 \log ^2(x)+\frac {147}{16} x^4 \log ^2(x)+\frac {43}{10} x^5 \log ^2(x)+\frac {1}{4} x^6 \log ^2(x)-\frac {1}{4} x^4 \log ^3(x)+\frac {1}{4} x^4 \log ^4(x)-\frac {3}{8} \int x^3 \log (x) \, dx-\frac {1}{2} \int x^5 \log (x) \, dx+\frac {5}{2} \int x^4 \log ^3(x) \, dx-\frac {9}{2} \int x \log (x) \, dx+\frac {9}{2} \int x^2 \log ^3(x) \, dx-\frac {43}{5} \int x^4 \log (x) \, dx+9 \int x^3 \log ^3(x) \, dx-15 \int x^2 \log (x) \, dx-18 \int x^3 \log (x) \, dx\\ &=-e^x+\frac {x^3}{3}+\frac {539 x^4}{128}+\frac {1003 x^5}{125}+4 x^6+5 x^3 \log (x)+\frac {421}{32} x^4 \log (x)+\frac {247}{25} x^5 \log (x)+2 x^6 \log (x)+\frac {9}{4} x^2 \log ^2(x)+\frac {15}{2} x^3 \log ^2(x)+\frac {147}{16} x^4 \log ^2(x)+\frac {43}{10} x^5 \log ^2(x)+\frac {1}{4} x^6 \log ^2(x)+\frac {3}{2} x^3 \log ^3(x)+2 x^4 \log ^3(x)+\frac {1}{2} x^5 \log ^3(x)+\frac {1}{4} x^4 \log ^4(x)-\frac {3}{2} \int x^4 \log ^2(x) \, dx-\frac {9}{2} \int x^2 \log ^2(x) \, dx-\frac {27}{4} \int x^3 \log ^2(x) \, dx\\ &=-e^x+\frac {x^3}{3}+\frac {539 x^4}{128}+\frac {1003 x^5}{125}+4 x^6+5 x^3 \log (x)+\frac {421}{32} x^4 \log (x)+\frac {247}{25} x^5 \log (x)+2 x^6 \log (x)+\frac {9}{4} x^2 \log ^2(x)+6 x^3 \log ^2(x)+\frac {15}{2} x^4 \log ^2(x)+4 x^5 \log ^2(x)+\frac {1}{4} x^6 \log ^2(x)+\frac {3}{2} x^3 \log ^3(x)+2 x^4 \log ^3(x)+\frac {1}{2} x^5 \log ^3(x)+\frac {1}{4} x^4 \log ^4(x)+\frac {3}{5} \int x^4 \log (x) \, dx+3 \int x^2 \log (x) \, dx+\frac {27}{8} \int x^3 \log (x) \, dx\\ &=-e^x+4 x^4+8 x^5+4 x^6+6 x^3 \log (x)+14 x^4 \log (x)+10 x^5 \log (x)+2 x^6 \log (x)+\frac {9}{4} x^2 \log ^2(x)+6 x^3 \log ^2(x)+\frac {15}{2} x^4 \log ^2(x)+4 x^5 \log ^2(x)+\frac {1}{4} x^6 \log ^2(x)+\frac {3}{2} x^3 \log ^3(x)+2 x^4 \log ^3(x)+\frac {1}{2} x^5 \log ^3(x)+\frac {1}{4} x^4 \log ^4(x)\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(89\) vs. \(2(34)=68\).
time = 0.08, size = 89, normalized size = 2.62 \begin {gather*} \frac {1}{4} \left (4 \left (-e^x+4 x^4 (1+x)^2\right )+8 x^3 (1+x)^2 (3+x) \log (x)+x^2 \left (9+24 x+30 x^2+16 x^3+x^4\right ) \log ^2(x)+2 x^3 \left (3+4 x+x^2\right ) \log ^3(x)+x^4 \log ^4(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*E^x + 12*x^2 + 60*x^3 + 100*x^4 + 52*x^5 + (9*x + 60*x^2 + 142*x^3 + 116*x^4 + 25*x^5)*Log[x] +
(9*x + 45*x^2 + 72*x^3 + 43*x^4 + 3*x^5)*Log[x]^2 + (9*x^2 + 18*x^3 + 5*x^4)*Log[x]^3 + 2*x^3*Log[x]^4)/2,x]

[Out]

(4*(-E^x + 4*x^4*(1 + x)^2) + 8*x^3*(1 + x)^2*(3 + x)*Log[x] + x^2*(9 + 24*x + 30*x^2 + 16*x^3 + x^4)*Log[x]^2
+ 2*x^3*(3 + 4*x + x^2)*Log[x]^3 + x^4*Log[x]^4)/4

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(129\) vs. \(2(31)=62\).
time = 0.43, size = 130, normalized size = 3.82

method	result	size
default	\(\frac {x^{6} \ln \left (x \right )^{2}}{4}+2 x^{6} \ln \left (x \right )+2 x^{4} \ln \left (x \right )^{3}+\frac {x^{5} \ln \left (x \right )^{3}}{2}+\frac {3 x^{3} \ln \left (x \right )^{3}}{2}+10 x^{5} \ln \left (x \right )+\frac {15 x^{4} \ln \left (x \right )^{2}}{2}+14 x^{4} \ln \left (x \right )+\frac {x^{4} \ln \left (x \right )^{4}}{4}+4 x^{5} \ln \left (x \right )^{2}+6 x^{3} \ln \left (x \right )^{2}+\frac {9 x^{2} \ln \left (x \right )^{2}}{4}+6 x^{3} \ln \left (x \right )+4 x^{6}+8 x^{5}+4 x^{4}-{\mathrm e}^{x}\)	\(130\)
risch	\(\frac {x^{6} \ln \left (x \right )^{2}}{4}+2 x^{6} \ln \left (x \right )+2 x^{4} \ln \left (x \right )^{3}+\frac {x^{5} \ln \left (x \right )^{3}}{2}+\frac {3 x^{3} \ln \left (x \right )^{3}}{2}+10 x^{5} \ln \left (x \right )+\frac {15 x^{4} \ln \left (x \right )^{2}}{2}+14 x^{4} \ln \left (x \right )+\frac {x^{4} \ln \left (x \right )^{4}}{4}+4 x^{5} \ln \left (x \right )^{2}+6 x^{3} \ln \left (x \right )^{2}+\frac {9 x^{2} \ln \left (x \right )^{2}}{4}+6 x^{3} \ln \left (x \right )+4 x^{6}+8 x^{5}+4 x^{4}-{\mathrm e}^{x}\)	\(130\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3*ln(x)^4+1/2*(5*x^4+18*x^3+9*x^2)*ln(x)^3+1/2*(3*x^5+43*x^4+72*x^3+45*x^2+9*x)*ln(x)^2+1/2*(25*x^5+116*
x^4+142*x^3+60*x^2+9*x)*ln(x)-exp(x)+26*x^5+50*x^4+30*x^3+6*x^2,x,method=_RETURNVERBOSE)

[Out]

1/4*x^6*ln(x)^2+2*x^6*ln(x)+2*x^4*ln(x)^3+1/2*x^5*ln(x)^3+3/2*x^3*ln(x)^3+10*x^5*ln(x)+15/2*x^4*ln(x)^2+14*x^4
*ln(x)+1/4*x^4*ln(x)^4+4*x^5*ln(x)^2+6*x^3*ln(x)^2+9/4*x^2*ln(x)^2+6*x^3*ln(x)+4*x^6+8*x^5+4*x^4-exp(x)

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 243 vs. \(2 (27) = 54\).
time = 0.29, size = 243, normalized size = 7.15 \begin {gather*} \frac {1}{72} \, {\left (18 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 1\right )} x^{6} + \frac {1}{250} \, {\left (125 \, \log \left (x\right )^{3} - 75 \, \log \left (x\right )^{2} + 30 \, \log \left (x\right ) - 6\right )} x^{5} + \frac {43}{250} \, {\left (25 \, \log \left (x\right )^{2} - 10 \, \log \left (x\right ) + 2\right )} x^{5} + \frac {287}{72} \, x^{6} + \frac {1}{128} \, {\left (32 \, \log \left (x\right )^{4} - 32 \, \log \left (x\right )^{3} + 24 \, \log \left (x\right )^{2} - 12 \, \log \left (x\right ) + 3\right )} x^{4} + \frac {9}{128} \, {\left (32 \, \log \left (x\right )^{3} - 24 \, \log \left (x\right )^{2} + 12 \, \log \left (x\right ) - 3\right )} x^{4} + \frac {9}{8} \, {\left (8 \, \log \left (x\right )^{2} - 4 \, \log \left (x\right ) + 1\right )} x^{4} + \frac {192}{25} \, x^{5} + \frac {1}{6} \, {\left (9 \, \log \left (x\right )^{3} - 9 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) - 2\right )} x^{3} + \frac {5}{6} \, {\left (9 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 2\right )} x^{3} + \frac {49}{16} \, x^{4} + \frac {9}{8} \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} - \frac {4}{3} \, x^{3} - \frac {9}{8} \, x^{2} + \frac {1}{60} \, {\left (125 \, x^{6} + 696 \, x^{5} + 1065 \, x^{4} + 600 \, x^{3} + 135 \, x^{2}\right )} \log \left (x\right ) - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3*log(x)^4+1/2*(5*x^4+18*x^3+9*x^2)*log(x)^3+1/2*(3*x^5+43*x^4+72*x^3+45*x^2+9*x)*log(x)^2+1/2*(25
*x^5+116*x^4+142*x^3+60*x^2+9*x)*log(x)-exp(x)+26*x^5+50*x^4+30*x^3+6*x^2,x, algorithm="maxima")

[Out]

1/72*(18*log(x)^2 - 6*log(x) + 1)*x^6 + 1/250*(125*log(x)^3 - 75*log(x)^2 + 30*log(x) - 6)*x^5 + 43/250*(25*lo
g(x)^2 - 10*log(x) + 2)*x^5 + 287/72*x^6 + 1/128*(32*log(x)^4 - 32*log(x)^3 + 24*log(x)^2 - 12*log(x) + 3)*x^4
+ 9/128*(32*log(x)^3 - 24*log(x)^2 + 12*log(x) - 3)*x^4 + 9/8*(8*log(x)^2 - 4*log(x) + 1)*x^4 + 192/25*x^5 +
1/6*(9*log(x)^3 - 9*log(x)^2 + 6*log(x) - 2)*x^3 + 5/6*(9*log(x)^2 - 6*log(x) + 2)*x^3 + 49/16*x^4 + 9/8*(2*lo
g(x)^2 - 2*log(x) + 1)*x^2 - 4/3*x^3 - 9/8*x^2 + 1/60*(125*x^6 + 696*x^5 + 1065*x^4 + 600*x^3 + 135*x^2)*log(x
) - e^x

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (27) = 54\).
time = 0.38, size = 102, normalized size = 3.00 \begin {gather*} \frac {1}{4} \, x^{4} \log \left (x\right )^{4} + 4 \, x^{6} + 8 \, x^{5} + 4 \, x^{4} + \frac {1}{2} \, {\left (x^{5} + 4 \, x^{4} + 3 \, x^{3}\right )} \log \left (x\right )^{3} + \frac {1}{4} \, {\left (x^{6} + 16 \, x^{5} + 30 \, x^{4} + 24 \, x^{3} + 9 \, x^{2}\right )} \log \left (x\right )^{2} + 2 \, {\left (x^{6} + 5 \, x^{5} + 7 \, x^{4} + 3 \, x^{3}\right )} \log \left (x\right ) - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3*log(x)^4+1/2*(5*x^4+18*x^3+9*x^2)*log(x)^3+1/2*(3*x^5+43*x^4+72*x^3+45*x^2+9*x)*log(x)^2+1/2*(25
*x^5+116*x^4+142*x^3+60*x^2+9*x)*log(x)-exp(x)+26*x^5+50*x^4+30*x^3+6*x^2,x, algorithm="fricas")

[Out]

1/4*x^4*log(x)^4 + 4*x^6 + 8*x^5 + 4*x^4 + 1/2*(x^5 + 4*x^4 + 3*x^3)*log(x)^3 + 1/4*(x^6 + 16*x^5 + 30*x^4 + 2
4*x^3 + 9*x^2)*log(x)^2 + 2*(x^6 + 5*x^5 + 7*x^4 + 3*x^3)*log(x) - e^x

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (26) = 52\).
time = 0.15, size = 107, normalized size = 3.15 \begin {gather*} 4 x^{6} + 8 x^{5} + \frac {x^{4} \log {\left (x \right )}^{4}}{4} + 4 x^{4} + \left (\frac {x^{5}}{2} + 2 x^{4} + \frac {3 x^{3}}{2}\right ) \log {\left (x \right )}^{3} + \left (2 x^{6} + 10 x^{5} + 14 x^{4} + 6 x^{3}\right ) \log {\left (x \right )} + \left (\frac {x^{6}}{4} + 4 x^{5} + \frac {15 x^{4}}{2} + 6 x^{3} + \frac {9 x^{2}}{4}\right ) \log {\left (x \right )}^{2} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**3*ln(x)**4+1/2*(5*x**4+18*x**3+9*x**2)*ln(x)**3+1/2*(3*x**5+43*x**4+72*x**3+45*x**2+9*x)*ln(x)**2
+1/2*(25*x**5+116*x**4+142*x**3+60*x**2+9*x)*ln(x)-exp(x)+26*x**5+50*x**4+30*x**3+6*x**2,x)

[Out]

4*x**6 + 8*x**5 + x**4*log(x)**4/4 + 4*x**4 + (x**5/2 + 2*x**4 + 3*x**3/2)*log(x)**3 + (2*x**6 + 10*x**5 + 14*
x**4 + 6*x**3)*log(x) + (x**6/4 + 4*x**5 + 15*x**4/2 + 6*x**3 + 9*x**2/4)*log(x)**2 - exp(x)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (27) = 54\).
time = 0.41, size = 129, normalized size = 3.79 \begin {gather*} \frac {1}{4} \, x^{6} \log \left (x\right )^{2} + \frac {1}{2} \, x^{5} \log \left (x\right )^{3} + \frac {1}{4} \, x^{4} \log \left (x\right )^{4} + 2 \, x^{6} \log \left (x\right ) + 4 \, x^{5} \log \left (x\right )^{2} + 2 \, x^{4} \log \left (x\right )^{3} + 4 \, x^{6} + 10 \, x^{5} \log \left (x\right ) + \frac {15}{2} \, x^{4} \log \left (x\right )^{2} + \frac {3}{2} \, x^{3} \log \left (x\right )^{3} + 8 \, x^{5} + 14 \, x^{4} \log \left (x\right ) + 6 \, x^{3} \log \left (x\right )^{2} + 4 \, x^{4} + 6 \, x^{3} \log \left (x\right ) + \frac {9}{4} \, x^{2} \log \left (x\right )^{2} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^3*log(x)^4+1/2*(5*x^4+18*x^3+9*x^2)*log(x)^3+1/2*(3*x^5+43*x^4+72*x^3+45*x^2+9*x)*log(x)^2+1/2*(25
*x^5+116*x^4+142*x^3+60*x^2+9*x)*log(x)-exp(x)+26*x^5+50*x^4+30*x^3+6*x^2,x, algorithm="giac")

[Out]

1/4*x^6*log(x)^2 + 1/2*x^5*log(x)^3 + 1/4*x^4*log(x)^4 + 2*x^6*log(x) + 4*x^5*log(x)^2 + 2*x^4*log(x)^3 + 4*x^
6 + 10*x^5*log(x) + 15/2*x^4*log(x)^2 + 3/2*x^3*log(x)^3 + 8*x^5 + 14*x^4*log(x) + 6*x^3*log(x)^2 + 4*x^4 + 6*
x^3*log(x) + 9/4*x^2*log(x)^2 - e^x

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Mupad [B]
time = 3.58, size = 105, normalized size = 3.09 \begin {gather*} {\ln \left (x\right )}^2\,\left (\frac {x^6}{4}+4\,x^5+\frac {15\,x^4}{2}+6\,x^3+\frac {9\,x^2}{4}\right )-{\mathrm {e}}^x+\frac {x^4\,{\ln \left (x\right )}^4}{4}+\ln \left (x\right )\,\left (2\,x^6+10\,x^5+14\,x^4+6\,x^3\right )+{\ln \left (x\right )}^3\,\left (\frac {x^5}{2}+2\,x^4+\frac {3\,x^3}{2}\right )+4\,x^4+8\,x^5+4\,x^6 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(9*x + 60*x^2 + 142*x^3 + 116*x^4 + 25*x^5))/2 - exp(x) + x^3*log(x)^4 + (log(x)^3*(9*x^2 + 18*x^3
+ 5*x^4))/2 + (log(x)^2*(9*x + 45*x^2 + 72*x^3 + 43*x^4 + 3*x^5))/2 + 6*x^2 + 30*x^3 + 50*x^4 + 26*x^5,x)

[Out]

log(x)^2*((9*x^2)/4 + 6*x^3 + (15*x^4)/2 + 4*x^5 + x^6/4) - exp(x) + (x^4*log(x)^4)/4 + log(x)*(6*x^3 + 14*x^4
+ 10*x^5 + 2*x^6) + log(x)^3*((3*x^3)/2 + 2*x^4 + x^5/2) + 4*x^4 + 8*x^5 + 4*x^6

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