3.73.80 $\int \frac{135-72x+90x^2-12x^3-x^4+4x^6+e^{2e^2}(15-3x^2)+e^{2x}(15-6x-3x^2+2x^3)+e^x(-90+42x-24x^2+2x^3+6x^4-4x^5)+e^{e^2}(-90+24x-18x^2-4x^3+4x^4+e^x(30-6x-6x^2+2x^3))}{x^6}dx$

Optimal. Leaf size=34 $${(-2-\frac{3-e^{e^2}-e^x-x}{x^2})}^2(-\frac{3}{x}+x)$$

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Rubi [C]  time = 0.93, antiderivative size = 406, normalized size of antiderivative = 11.94, number of steps used = 47, number of rules used = 4, integrand size = 139, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.029, Rules used = {14, 2199, 2177, 2178} $$\begin{array}{c}-(4+e^{e^2})\text{Ei}(x)+(1+e^{e^2})\text{Ei}(x)+\frac{1}{4}(7-e^{e^2})\text{Ei}(x)-\frac{1}{4}(3-e^{e^2})\text{Ei}(x)+2\text{Ei}(x)-\frac{3e^{2x}}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})e^x}{x^5}-\frac{3(7-e^{e^2})e^x}{2x^4}+\frac{3(3-e^{e^2})e^x}{2x^4}+\frac{6(3-e^{e^2})}{x^4}+\frac{e^{2x}}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{2(4+e^{e^2})e^x}{x^3}-\frac{(7-e^{e^2})e^x}{2x^3}+\frac{(3-e^{e^2})e^x}{2x^3}+\frac{(4+e^{e^2})e^x}{x^2}+\frac{2(3+e^{e^2})}{x^2}-\frac{(1+e^{e^2})e^x}{x^2}-\frac{(7-e^{e^2})e^x}{4x^2}+\frac{(3-e^{e^2})e^x}{4x^2}+4x-\frac{6e^x}{x}+\frac{(4+e^{e^2})e^x}{x}-\frac{(1+e^{e^2})e^x}{x}-\frac{(7-e^{e^2})e^x}{4x}+\frac{(3-e^{e^2})e^x}{4x}+\frac{1-4e^{e^2}}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(135 - 72*x + 90*x^2 - 12*x^3 - x^4 + 4*x^6 + E^(2*E^2)*(15 - 3*x^2) + E^(2*x)*(15 - 6*x - 3*x^2 + 2*x^3)
+ E^x*(-90 + 42*x - 24*x^2 + 2*x^3 + 6*x^4 - 4*x^5) + E^E^2*(-90 + 24*x - 18*x^2 - 4*x^3 + 4*x^4 + E^x*(30 - 6
*x - 6*x^2 + 2*x^3)))/x^6,x]

[Out]

(-3*E^(2*x))/x^5 + (6*E^x*(3 - E^E^2))/x^5 - (3*(3 - E^E^2)^2)/x^5 + (6*(3 - E^E^2))/x^4 + (3*E^x*(3 - E^E^2))
/(2*x^4) - (3*E^x*(7 - E^E^2))/(2*x^4) + E^(2*x)/x^3 + (E^x*(3 - E^E^2))/(2*x^3) - (E^x*(7 - E^E^2))/(2*x^3) +
(2*E^x*(4 + E^E^2))/x^3 - (30 - 6*E^E^2 - E^(2*E^2))/x^3 + (E^x*(3 - E^E^2))/(4*x^2) - (E^x*(7 - E^E^2))/(4*x
^2) - (E^x*(1 + E^E^2))/x^2 + (2*(3 + E^E^2))/x^2 + (E^x*(4 + E^E^2))/x^2 - (6*E^x)/x + (1 - 4*E^E^2)/x + (E^x
*(3 - E^E^2))/(4*x) - (E^x*(7 - E^E^2))/(4*x) - (E^x*(1 + E^E^2))/x + (E^x*(4 + E^E^2))/x + 4*x + 2*ExpIntegra
lEi[x] - ((3 - E^E^2)*ExpIntegralEi[x])/4 + ((7 - E^E^2)*ExpIntegralEi[x])/4 + (1 + E^E^2)*ExpIntegralEi[x] -
(4 + E^E^2)*ExpIntegralEi[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 2177

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[((c + d*x)^(m
+ 1)*(b*F^(g*(e + f*x)))^n)/(d*(m + 1)), x] - Dist[(f*g*n*Log[F])/(d*(m + 1)), 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] && LtQ[m, -1] && IntegerQ[2*m] &&  !$UseGamma ===
True

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2199

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), w*NormalizePo
werOfLinear[u, x]^m, x], x] /; FreeQ[{F, c}, x] && PolynomialQ[w, x] && LinearQ[v, x] && PowerOfLinearQ[u, x]
&& IntegerQ[m] &&  !$UseGamma === True

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (\frac{e^{2x}(15-6x-3x^2+2x^3)}{x^6}+\frac{2e^x(-45(1-\frac{e^{e^2}}{3})+21(1-\frac{e^{e^2}}{7})x-12(1+\frac{e^{e^2}}{4})x^2+(1+e^{e^2})x^3+3x^4-2x^5)}{x^6}+\frac{135(1+\frac{1}{9}{e}^{e^2}(-6+e^{e^2}))-72(1-\frac{e^{e^2}}{3})x+90(1-\frac{1}{30}{e}^{e^2}(6+e^{e^2}))x^2-12(1+\frac{e^{e^2}}{3})x^3-(1-4e^{e^2})x^4+4x^6}{x^6})dx\\ & =2\int \frac{e^x(-45(1-\frac{e^{e^2}}{3})+21(1-\frac{e^{e^2}}{7})x-12(1+\frac{e^{e^2}}{4})x^2+(1+e^{e^2})x^3+3x^4-2x^5)}{x^6}dx+\int \frac{e^{2x}(15-6x-3x^2+2x^3)}{x^6}dx+\int \frac{135(1+\frac{1}{9}{e}^{e^2}(-6+e^{e^2}))-72(1-\frac{e^{e^2}}{3})x+90(1-\frac{1}{30}{e}^{e^2}(6+e^{e^2}))x^2-12(1+\frac{e^{e^2}}{3})x^3-(1-4e^{e^2})x^4+4x^6}{x^6}dx\\ & =2\int (\frac{15e^x(-3+e^{e^2})}{x^6}-\frac{3e^x(-7+e^{e^2})}{x^5}-\frac{3e^x(4+e^{e^2})}{x^4}+\frac{e^x(1+e^{e^2})}{x^3}+\frac{3e^x}{x^2}-\frac{2e^x}{x})dx+\int (\frac{15e^{2x}}{x^6}-\frac{6e^{2x}}{x^5}-\frac{3e^{2x}}{x^4}+\frac{2e^{2x}}{x^3})dx+\int (4+\frac{15{(-3+e^{e^2})}^2}{x^6}+\frac{24(-3+e^{e^2})}{x^5}-\frac{3(-30+6e^{e^2}+e^{2e^2})}{x^4}-\frac{4(3+e^{e^2})}{x^3}+\frac{-1+4e^{e^2}}{x^2})dx\\ & =-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{2(3+e^{e^2})}{x^2}+\frac{1-4e^{e^2}}{x}+4x+2\int \frac{e^{2x}}{x^3}dx-3\int \frac{e^{2x}}{x^4}dx-4\int \frac{e^x}{x}dx-6\int \frac{e^{2x}}{x^5}dx+6\int \frac{e^x}{x^2}dx+15\int \frac{e^{2x}}{x^6}dx-\left(30(3-e^{e^2})\right)\int \frac{e^x}{x^6}dx+\left(6(7-e^{e^2})\right)\int \frac{e^x}{x^5}dx+\left(2(1+e^{e^2})\right)\int \frac{e^x}{x^3}dx-\left(6(4+e^{e^2})\right)\int \frac{e^x}{x^4}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{3e^{2x}}{2x^4}+\frac{6(3-e^{e^2})}{x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{e^{2x}}{x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}-\frac{e^{2x}}{x^2}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}-\frac{6e^x}{x}+\frac{1-4e^{e^2}}{x}+4x-4\text{Ei}(x)-2\int \frac{e^{2x}}{x^3}dx+2\int \frac{e^{2x}}{x^2}dx-3\int \frac{e^{2x}}{x^4}dx+6\int \frac{e^{2x}}{x^5}dx+6\int \frac{e^x}{x}dx-\left(6(3-e^{e^2})\right)\int \frac{e^x}{x^5}dx+\frac{1}{2}\left(3(7-e^{e^2})\right)\int \frac{e^x}{x^4}dx+(1+e^{e^2})\int \frac{e^x}{x^2}dx-\left(2(4+e^{e^2})\right)\int \frac{e^x}{x^3}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}+\frac{3e^x(3-e^{e^2})}{2x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{2e^{2x}}{x^3}-\frac{e^x(7-e^{e^2})}{2x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}+\frac{e^x(4+e^{e^2})}{x^2}-\frac{6e^x}{x}-\frac{2e^{2x}}{x}+\frac{1-4e^{e^2}}{x}-\frac{e^x(1+e^{e^2})}{x}+4x+2\text{Ei}(x)-2\int \frac{e^{2x}}{x^3}dx-2\int \frac{e^{2x}}{x^2}dx+3\int \frac{e^{2x}}{x^4}dx+4\int \frac{e^{2x}}{x}dx-\frac{1}{2}\left(3(3-e^{e^2})\right)\int \frac{e^x}{x^4}dx+\frac{1}{2}(7-e^{e^2})\int \frac{e^x}{x^3}dx+(1+e^{e^2})\int \frac{e^x}{x}dx-(4+e^{e^2})\int \frac{e^x}{x^2}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}+\frac{3e^x(3-e^{e^2})}{2x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{e^{2x}}{x^3}+\frac{e^x(3-e^{e^2})}{2x^3}-\frac{e^x(7-e^{e^2})}{2x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{e^{2x}}{x^2}-\frac{e^x(7-e^{e^2})}{4x^2}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}+\frac{e^x(4+e^{e^2})}{x^2}-\frac{6e^x}{x}+\frac{1-4e^{e^2}}{x}-\frac{e^x(1+e^{e^2})}{x}+\frac{e^x(4+e^{e^2})}{x}+4x+2\text{Ei}(x)+(1+e^{e^2})\text{Ei}(x)+4\text{Ei}(2x)+2\int \frac{e^{2x}}{x^3}dx-2\int \frac{e^{2x}}{x^2}dx-4\int \frac{e^{2x}}{x}dx-\frac{1}{2}(3-e^{e^2})\int \frac{e^x}{x^3}dx+\frac{1}{4}(7-e^{e^2})\int \frac{e^x}{x^2}dx-(4+e^{e^2})\int \frac{e^x}{x}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}+\frac{3e^x(3-e^{e^2})}{2x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{e^{2x}}{x^3}+\frac{e^x(3-e^{e^2})}{2x^3}-\frac{e^x(7-e^{e^2})}{2x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{e^x(3-e^{e^2})}{4x^2}-\frac{e^x(7-e^{e^2})}{4x^2}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}+\frac{e^x(4+e^{e^2})}{x^2}-\frac{6e^x}{x}+\frac{2e^{2x}}{x}+\frac{1-4e^{e^2}}{x}-\frac{e^x(7-e^{e^2})}{4x}-\frac{e^x(1+e^{e^2})}{x}+\frac{e^x(4+e^{e^2})}{x}+4x+2\text{Ei}(x)+(1+e^{e^2})\text{Ei}(x)-(4+e^{e^2})\text{Ei}(x)+2\int \frac{e^{2x}}{x^2}dx-4\int \frac{e^{2x}}{x}dx-\frac{1}{4}(3-e^{e^2})\int \frac{e^x}{x^2}dx+\frac{1}{4}(7-e^{e^2})\int \frac{e^x}{x}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}+\frac{3e^x(3-e^{e^2})}{2x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{e^{2x}}{x^3}+\frac{e^x(3-e^{e^2})}{2x^3}-\frac{e^x(7-e^{e^2})}{2x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{e^x(3-e^{e^2})}{4x^2}-\frac{e^x(7-e^{e^2})}{4x^2}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}+\frac{e^x(4+e^{e^2})}{x^2}-\frac{6e^x}{x}+\frac{1-4e^{e^2}}{x}+\frac{e^x(3-e^{e^2})}{4x}-\frac{e^x(7-e^{e^2})}{4x}-\frac{e^x(1+e^{e^2})}{x}+\frac{e^x(4+e^{e^2})}{x}+4x+2\text{Ei}(x)+\frac{1}{4}(7-e^{e^2})\text{Ei}(x)+(1+e^{e^2})\text{Ei}(x)-(4+e^{e^2})\text{Ei}(x)-4\text{Ei}(2x)+4\int \frac{e^{2x}}{x}dx-\frac{1}{4}(3-e^{e^2})\int \frac{e^x}{x}dx\\ & =-\frac{3e^{2x}}{x^5}+\frac{6e^x(3-e^{e^2})}{x^5}-\frac{3{(3-e^{e^2})}^2}{x^5}+\frac{6(3-e^{e^2})}{x^4}+\frac{3e^x(3-e^{e^2})}{2x^4}-\frac{3e^x(7-e^{e^2})}{2x^4}+\frac{e^{2x}}{x^3}+\frac{e^x(3-e^{e^2})}{2x^3}-\frac{e^x(7-e^{e^2})}{2x^3}+\frac{2e^x(4+e^{e^2})}{x^3}-\frac{30-6e^{e^2}-e^{2e^2}}{x^3}+\frac{e^x(3-e^{e^2})}{4x^2}-\frac{e^x(7-e^{e^2})}{4x^2}-\frac{e^x(1+e^{e^2})}{x^2}+\frac{2(3+e^{e^2})}{x^2}+\frac{e^x(4+e^{e^2})}{x^2}-\frac{6e^x}{x}+\frac{1-4e^{e^2}}{x}+\frac{e^x(3-e^{e^2})}{4x}-\frac{e^x(7-e^{e^2})}{4x}-\frac{e^x(1+e^{e^2})}{x}+\frac{e^x(4+e^{e^2})}{x}+4x+2\text{Ei}(x)-\frac{1}{4}(3-e^{e^2})\text{Ei}(x)+\frac{1}{4}(7-e^{e^2})\text{Ei}(x)+(1+e^{e^2})\text{Ei}(x)-(4+e^{e^2})\text{Ei}(x)\end{array}\end{array}$$

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Mathematica [B]  time = 0.09, size = 113, normalized size = 3.32 $$\begin{array}{c}\frac{-27+18x-30x^2+6x^3+x^4+4x^6+e^{2e^2}(-3+x^2)+e^{2x}(-3+x^2)+2e^{e^2+x}(-3+x^2)+2e^{e^2}(9-3x+3x^2+x^3-2x^4)+2e^x(9-3x+3x^2+x^3-2x^4)}{x^5}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(135 - 72*x + 90*x^2 - 12*x^3 - x^4 + 4*x^6 + E^(2*E^2)*(15 - 3*x^2) + E^(2*x)*(15 - 6*x - 3*x^2 + 2
*x^3) + E^x*(-90 + 42*x - 24*x^2 + 2*x^3 + 6*x^4 - 4*x^5) + E^E^2*(-90 + 24*x - 18*x^2 - 4*x^3 + 4*x^4 + E^x*(
30 - 6*x - 6*x^2 + 2*x^3)))/x^6,x]

[Out]

(-27 + 18*x - 30*x^2 + 6*x^3 + x^4 + 4*x^6 + E^(2*E^2)*(-3 + x^2) + E^(2*x)*(-3 + x^2) + 2*E^(E^2 + x)*(-3 + x
^2) + 2*E^E^2*(9 - 3*x + 3*x^2 + x^3 - 2*x^4) + 2*E^x*(9 - 3*x + 3*x^2 + x^3 - 2*x^4))/x^5

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fricas [B]  time = 0.74, size = 106, normalized size = 3.12 $$\begin{array}{c}\frac{4x^6+x^4+6x^3-30x^2+(x^2-3)e^{\left(2x\right)}-2(2x^4-x^3-3x^2+3x-9)e^x+(x^2-3)e^{\left(2e^2\right)}-2(2x^4-x^3-3x^2-(x^2-3)e^x+3x-9)e^{\left(e^2\right)}+18x-27}{x^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2+15)*exp(exp(2))^2+((2*x^3-6*x^2-6*x+30)*exp(x)+4*x^4-4*x^3-18*x^2+24*x-90)*exp(exp(2))+(2*x
^3-3*x^2-6*x+15)*exp(x)^2+(-4*x^5+6*x^4+2*x^3-24*x^2+42*x-90)*exp(x)+4*x^6-x^4-12*x^3+90*x^2-72*x+135)/x^6,x,
algorithm="fricas")

[Out]

(4*x^6 + x^4 + 6*x^3 - 30*x^2 + (x^2 - 3)*e^(2*x) - 2*(2*x^4 - x^3 - 3*x^2 + 3*x - 9)*e^x + (x^2 - 3)*e^(2*e^2
) - 2*(2*x^4 - x^3 - 3*x^2 - (x^2 - 3)*e^x + 3*x - 9)*e^(e^2) + 18*x - 27)/x^5

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giac [B]  time = 0.22, size = 139, normalized size = 4.09 $$\begin{array}{c}\frac{4x^6-4x^4{e}^x-4x^4{e}^{\left(e^2\right)}+x^4+2x^3{e}^x+2x^3{e}^{\left(e^2\right)}+6x^3+x^2{e}^{\left(2x\right)}+2x^2{e}^{(x+e^2)}+6x^2{e}^x+x^2{e}^{\left(2e^2\right)}+6x^2{e}^{\left(e^2\right)}-30x^2-6x{e}^x-6x{e}^{\left(e^2\right)}+18x-3e^{\left(2x\right)}-6e^{(x+e^2)}+18e^x-3e^{\left(2e^2\right)}+18e^{\left(e^2\right)}-27}{x^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2+15)*exp(exp(2))^2+((2*x^3-6*x^2-6*x+30)*exp(x)+4*x^4-4*x^3-18*x^2+24*x-90)*exp(exp(2))+(2*x
^3-3*x^2-6*x+15)*exp(x)^2+(-4*x^5+6*x^4+2*x^3-24*x^2+42*x-90)*exp(x)+4*x^6-x^4-12*x^3+90*x^2-72*x+135)/x^6,x,
algorithm="giac")

[Out]

(4*x^6 - 4*x^4*e^x - 4*x^4*e^(e^2) + x^4 + 2*x^3*e^x + 2*x^3*e^(e^2) + 6*x^3 + x^2*e^(2*x) + 2*x^2*e^(x + e^2)
+ 6*x^2*e^x + x^2*e^(2*e^2) + 6*x^2*e^(e^2) - 30*x^2 - 6*x*e^x - 6*x*e^(e^2) + 18*x - 3*e^(2*x) - 6*e^(x + e^
2) + 18*e^x - 3*e^(2*e^2) + 18*e^(e^2) - 27)/x^5

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maple [B]  time = 0.07, size = 120, normalized size = 3.53

method	result	size
risch	$4x+\frac{(-4{\mathrm{e}}^{{\mathrm{e}}^2}+1)x^4+(6+2{\mathrm{e}}^{{\mathrm{e}}^2})x^3+({\mathrm{e}}^{2{\mathrm{e}}^2}+6{\mathrm{e}}^{{\mathrm{e}}^2}-30)x^2+(18-6{\mathrm{e}}^{{\mathrm{e}}^2})x-3{\mathrm{e}}^{2{\mathrm{e}}^2}+18{\mathrm{e}}^{{\mathrm{e}}^2}-27}{x^5}+\frac{(x^2-3){\mathrm{e}}^{2x}}{x^5}+\frac{2(-2x^4+x^2{\mathrm{e}}^{{\mathrm{e}}^2}+x^3+3x^2-3{\mathrm{e}}^{{\mathrm{e}}^2}-3x+9){\mathrm{e}}^x}{x^5}$	$120$
norman	$\frac{(6+2{\mathrm{e}}^{{\mathrm{e}}^2})x^3+(18-6{\mathrm{e}}^{{\mathrm{e}}^2})x+(18-6{\mathrm{e}}^{{\mathrm{e}}^2}){\mathrm{e}}^x+(-4{\mathrm{e}}^{{\mathrm{e}}^2}+1)x^4+({\mathrm{e}}^{2{\mathrm{e}}^2}+6{\mathrm{e}}^{{\mathrm{e}}^2}-30)x^2+{\mathrm{e}}^{2x}{x}^2+(6+2{\mathrm{e}}^{{\mathrm{e}}^2})x^2{\mathrm{e}}^x+4x^6-3{\mathrm{e}}^{2x}-6{\mathrm{e}}^{x}x+2{\mathrm{e}}^x{x}^3-4{\mathrm{e}}^x{x}^4-3{\mathrm{e}}^{2{\mathrm{e}}^2}+18{\mathrm{e}}^{{\mathrm{e}}^2}-27}{x^5}$	$127$
default	$4x-\frac{27}{x^5}+\frac{18}{x^4}-\frac{30}{x^3}+\frac{6}{x^2}+\frac{1}{x}+\frac{18{\mathrm{e}}^x}{x^5}-\frac{6{\mathrm{e}}^x}{x^4}+\frac{6{\mathrm{e}}^x}{x^3}+\frac{2{\mathrm{e}}^x}{x^2}-\frac{4{\mathrm{e}}^x}{x}+\frac{18{\mathrm{e}}^{{\mathrm{e}}^2}}{x^5}-\frac{3{\mathrm{e}}^{2{\mathrm{e}}^2}}{x^5}-\frac{6{\mathrm{e}}^{{\mathrm{e}}^2}}{x^4}+\frac{6{\mathrm{e}}^{{\mathrm{e}}^2}}{x^3}+\frac{2{\mathrm{e}}^{{\mathrm{e}}^2}}{x^2}-\frac{3{\mathrm{e}}^{2x}}{x^5}+\frac{{\mathrm{e}}^{2x}}{x^3}-\frac{4{\mathrm{e}}^{{\mathrm{e}}^2}}{x}+\frac{{\mathrm{e}}^{2{\mathrm{e}}^2}}{x^3}+30{\mathrm{e}}^{{\mathrm{e}}^2}(-\frac{{\mathrm{e}}^x}{5x^5}-\frac{{\mathrm{e}}^x}{20x^4}-\frac{{\mathrm{e}}^x}{60x^3}-\frac{{\mathrm{e}}^x}{120x^2}-\frac{{\mathrm{e}}^x}{120x}-\frac{\text{expIntegralEi}(1,-x)}{120})-6{\mathrm{e}}^{{\mathrm{e}}^2}(-\frac{{\mathrm{e}}^x}{4x^4}-\frac{{\mathrm{e}}^x}{12x^3}-\frac{{\mathrm{e}}^x}{24x^2}-\frac{{\mathrm{e}}^x}{24x}-\frac{\text{expIntegralEi}(1,-x)}{24})-6{\mathrm{e}}^{{\mathrm{e}}^2}(-\frac{{\mathrm{e}}^x}{3x^3}-\frac{{\mathrm{e}}^x}{6x^2}-\frac{{\mathrm{e}}^x}{6x}-\frac{\text{expIntegralEi}(1,-x)}{6})+2{\mathrm{e}}^{{\mathrm{e}}^2}(-\frac{{\mathrm{e}}^x}{2x^2}-\frac{{\mathrm{e}}^x}{2x}-\frac{\text{expIntegralEi}(1,-x)}{2})$	$289$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-3*x^2+15)*exp(exp(2))^2+((2*x^3-6*x^2-6*x+30)*exp(x)+4*x^4-4*x^3-18*x^2+24*x-90)*exp(exp(2))+(2*x^3-3*x
^2-6*x+15)*exp(x)^2+(-4*x^5+6*x^4+2*x^3-24*x^2+42*x-90)*exp(x)+4*x^6-x^4-12*x^3+90*x^2-72*x+135)/x^6,x,method=
_RETURNVERBOSE)

[Out]

4*x+((-4*exp(exp(2))+1)*x^4+(6+2*exp(exp(2)))*x^3+(exp(2*exp(2))+6*exp(exp(2))-30)*x^2+(18-6*exp(exp(2)))*x-3*
exp(2*exp(2))+18*exp(exp(2))-27)/x^5+(x^2-3)/x^5*exp(2*x)+2*(-2*x^4+x^2*exp(exp(2))+x^3+3*x^2-3*exp(exp(2))-3*
x+9)/x^5*exp(x)

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maxima [C]  time = 0.43, size = 193, normalized size = 5.68 $$\begin{array}{c}-2e^{\left(e^2\right)}\mathrm{\Gamma }(-2,-x)-6e^{\left(e^2\right)}\mathrm{\Gamma }(-3,-x)+6e^{\left(e^2\right)}\mathrm{\Gamma }(-4,-x)+30e^{\left(e^2\right)}\mathrm{\Gamma }(-5,-x)+4x-\frac{4e^{\left(e^2\right)}}{x}+\frac{1}{x}+\frac{2e^{\left(e^2\right)}}{x^2}+\frac{6}{x^2}+\frac{e^{\left(2e^2\right)}}{x^3}+\frac{6e^{\left(e^2\right)}}{x^3}-\frac{30}{x^3}-\frac{6e^{\left(e^2\right)}}{x^4}+\frac{18}{x^4}-\frac{3e^{\left(2e^2\right)}}{x^5}+\frac{18e^{\left(e^2\right)}}{x^5}-\frac{27}{x^5}-4\mathrm{E}\mathrm{i}(x)+6\mathrm{\Gamma }(-1,-x)-2\mathrm{\Gamma }(-2,-x)-8\mathrm{\Gamma }(-2,-2x)-24\mathrm{\Gamma }(-3,-x)-24\mathrm{\Gamma }(-3,-2x)-42\mathrm{\Gamma }(-4,-x)+96\mathrm{\Gamma }(-4,-2x)-90\mathrm{\Gamma }(-5,-x)+480\mathrm{\Gamma }(-5,-2x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x^2+15)*exp(exp(2))^2+((2*x^3-6*x^2-6*x+30)*exp(x)+4*x^4-4*x^3-18*x^2+24*x-90)*exp(exp(2))+(2*x
^3-3*x^2-6*x+15)*exp(x)^2+(-4*x^5+6*x^4+2*x^3-24*x^2+42*x-90)*exp(x)+4*x^6-x^4-12*x^3+90*x^2-72*x+135)/x^6,x,
algorithm="maxima")

[Out]

-2*e^(e^2)*gamma(-2, -x) - 6*e^(e^2)*gamma(-3, -x) + 6*e^(e^2)*gamma(-4, -x) + 30*e^(e^2)*gamma(-5, -x) + 4*x
- 4*e^(e^2)/x + 1/x + 2*e^(e^2)/x^2 + 6/x^2 + e^(2*e^2)/x^3 + 6*e^(e^2)/x^3 - 30/x^3 - 6*e^(e^2)/x^4 + 18/x^4
- 3*e^(2*e^2)/x^5 + 18*e^(e^2)/x^5 - 27/x^5 - 4*Ei(x) + 6*gamma(-1, -x) - 2*gamma(-2, -x) - 8*gamma(-2, -2*x)
- 24*gamma(-3, -x) - 24*gamma(-3, -2*x) - 42*gamma(-4, -x) + 96*gamma(-4, -2*x) - 90*gamma(-5, -x) + 480*gamma
(-5, -2*x)

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mupad [B]  time = 4.37, size = 96, normalized size = 2.82 $$\begin{array}{c}4x+\frac{{\mathrm{e}}^{2{\mathrm{e}}^2}+{\mathrm{e}}^{2x}+2{\mathrm{e}}^{x+{\mathrm{e}}^2}+6{\mathrm{e}}^{{\mathrm{e}}^2}+6{\mathrm{e}}^x-30}{x^3}-\frac{3{({\mathrm{e}}^{{\mathrm{e}}^2}+{\mathrm{e}}^x-3)}^2}{x^5}-\frac{4{\mathrm{e}}^{{\mathrm{e}}^2}+4{\mathrm{e}}^x-1}{x}+\frac{2{\mathrm{e}}^{{\mathrm{e}}^2}+2{\mathrm{e}}^x+6}{x^2}-\frac{6{\mathrm{e}}^{{\mathrm{e}}^2}+6{\mathrm{e}}^x-18}{x^4}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(72*x + exp(2*exp(2))*(3*x^2 - 15) + exp(2*x)*(6*x + 3*x^2 - 2*x^3 - 15) - exp(x)*(42*x - 24*x^2 + 2*x^3
+ 6*x^4 - 4*x^5 - 90) - 90*x^2 + 12*x^3 + x^4 - 4*x^6 + exp(exp(2))*(18*x^2 - 24*x + 4*x^3 - 4*x^4 + exp(x)*(6
*x + 6*x^2 - 2*x^3 - 30) + 90) - 135)/x^6,x)

[Out]

4*x + (exp(2*exp(2)) + exp(2*x) + 2*exp(x + exp(2)) + 6*exp(exp(2)) + 6*exp(x) - 30)/x^3 - (3*(exp(exp(2)) + e
xp(x) - 3)^2)/x^5 - (4*exp(exp(2)) + 4*exp(x) - 1)/x + (2*exp(exp(2)) + 2*exp(x) + 6)/x^2 - (6*exp(exp(2)) + 6
*exp(x) - 18)/x^4

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sympy [B]  time = 2.48, size = 141, normalized size = 4.15 $$\begin{array}{c}4x+\frac{x^4(1-4e^{e^2})+x^3(6+2e^{e^2})+x^2(-30+6e^{e^2}+e^{2e^2})+x(18-6e^{e^2})-3e^{2e^2}-27+18e^{e^2}}{x^5}+\frac{(x^7-3x^5)e^{2x}+(-4x^9+2x^8+6x^7+2x^7{e}^{e^2}-6x^6-6x^5{e}^{e^2}+18x^5)e^x}{x^{10}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*x**2+15)*exp(exp(2))**2+((2*x**3-6*x**2-6*x+30)*exp(x)+4*x**4-4*x**3-18*x**2+24*x-90)*exp(exp(2
))+(2*x**3-3*x**2-6*x+15)*exp(x)**2+(-4*x**5+6*x**4+2*x**3-24*x**2+42*x-90)*exp(x)+4*x**6-x**4-12*x**3+90*x**2
-72*x+135)/x**6,x)

[Out]

4*x + (x**4*(1 - 4*exp(exp(2))) + x**3*(6 + 2*exp(exp(2))) + x**2*(-30 + 6*exp(exp(2)) + exp(2*exp(2))) + x*(1
8 - 6*exp(exp(2))) - 3*exp(2*exp(2)) - 27 + 18*exp(exp(2)))/x**5 + ((x**7 - 3*x**5)*exp(2*x) + (-4*x**9 + 2*x*
*8 + 6*x**7 + 2*x**7*exp(exp(2)) - 6*x**6 - 6*x**5*exp(exp(2)) + 18*x**5)*exp(x))/x**10

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