3.81.71 \(\int \frac {-6 x^3-2 x^4-36 x^6-30 x^7-6 x^8+(-18-6 x) \log ^2(2)+e^{2 x} (-2 x^3-4 x^6-2 x^7+(-2+2 x) \log ^2(2))+e^x (8 x^3+2 x^4+24 x^6+16 x^7+2 x^8+(12-4 x-2 x^2) \log ^2(2))}{x^3} \, dx\)

Optimal. Leaf size=34 \[ \left (-\frac {e^x}{x}+\frac {3+x}{x}\right )^2 \left (-x^2-x^6+\log ^2(2)\right ) \]

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Rubi [B]  time = 0.55, antiderivative size = 123, normalized size of antiderivative = 3.62, number of steps used = 47, number of rules used = 7, integrand size = 117, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {14, 1620, 2199, 2194, 2176, 2177, 2178} \begin {gather*} -x^6+2 e^x x^5-6 x^5+6 e^x x^4-e^{2 x} x^4-9 x^4-x^2-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {9 \log ^2(2)}{x^2}+2 e^x x-6 x+6 e^x-e^{2 x}-\frac {2 e^x \log ^2(2)}{x}+\frac {6 \log ^2(2)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-6*x^3 - 2*x^4 - 36*x^6 - 30*x^7 - 6*x^8 + (-18 - 6*x)*Log[2]^2 + E^(2*x)*(-2*x^3 - 4*x^6 - 2*x^7 + (-2 +
2*x)*Log[2]^2) + E^x*(8*x^3 + 2*x^4 + 24*x^6 + 16*x^7 + 2*x^8 + (12 - 4*x - 2*x^2)*Log[2]^2))/x^3,x]

[Out]

6*E^x - E^(2*x) - 6*x + 2*E^x*x - x^2 - 9*x^4 + 6*E^x*x^4 - E^(2*x)*x^4 - 6*x^5 + 2*E^x*x^5 - x^6 + (9*Log[2]^
2)/x^2 - (6*E^x*Log[2]^2)/x^2 + (E^(2*x)*Log[2]^2)/x^2 + (6*Log[2]^2)/x - (2*E^x*Log[2]^2)/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 1620

Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)
^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2]) &&
GtQ[Expon[Px, x], 2]

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 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 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 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 {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (3+x) \left (x^3+6 x^6+3 x^7+3 \log ^2(2)\right )}{x^3}-\frac {2 e^{2 x} \left (x^3+2 x^6+x^7+\log ^2(2)-x \log ^2(2)\right )}{x^3}+\frac {2 e^x \left (4 x^3+x^4+12 x^6+8 x^7+x^8+6 \log ^2(2)-2 x \log ^2(2)-x^2 \log ^2(2)\right )}{x^3}\right ) \, dx\\ &=-\left (2 \int \frac {(3+x) \left (x^3+6 x^6+3 x^7+3 \log ^2(2)\right )}{x^3} \, dx\right )-2 \int \frac {e^{2 x} \left (x^3+2 x^6+x^7+\log ^2(2)-x \log ^2(2)\right )}{x^3} \, dx+2 \int \frac {e^x \left (4 x^3+x^4+12 x^6+8 x^7+x^8+6 \log ^2(2)-2 x \log ^2(2)-x^2 \log ^2(2)\right )}{x^3} \, dx\\ &=-\left (2 \int \left (3+x+18 x^3+15 x^4+3 x^5+\frac {9 \log ^2(2)}{x^3}+\frac {3 \log ^2(2)}{x^2}\right ) \, dx\right )-2 \int \left (e^{2 x}+2 e^{2 x} x^3+e^{2 x} x^4+\frac {e^{2 x} \log ^2(2)}{x^3}-\frac {e^{2 x} \log ^2(2)}{x^2}\right ) \, dx+2 \int \left (4 e^x+e^x x+12 e^x x^3+8 e^x x^4+e^x x^5+\frac {6 e^x \log ^2(2)}{x^3}-\frac {2 e^x \log ^2(2)}{x^2}-\frac {e^x \log ^2(2)}{x}\right ) \, dx\\ &=-6 x-x^2-9 x^4-6 x^5-x^6+\frac {9 \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-2 \int e^{2 x} \, dx+2 \int e^x x \, dx-2 \int e^{2 x} x^4 \, dx+2 \int e^x x^5 \, dx-4 \int e^{2 x} x^3 \, dx+8 \int e^x \, dx+16 \int e^x x^4 \, dx+24 \int e^x x^3 \, dx-\left (2 \log ^2(2)\right ) \int \frac {e^{2 x}}{x^3} \, dx+\left (2 \log ^2(2)\right ) \int \frac {e^{2 x}}{x^2} \, dx-\left (2 \log ^2(2)\right ) \int \frac {e^x}{x} \, dx-\left (4 \log ^2(2)\right ) \int \frac {e^x}{x^2} \, dx+\left (12 \log ^2(2)\right ) \int \frac {e^x}{x^3} \, dx\\ &=8 e^x-e^{2 x}-6 x+2 e^x x-x^2+24 e^x x^3-2 e^{2 x} x^3-9 x^4+16 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}+\frac {4 e^x \log ^2(2)}{x}-\frac {2 e^{2 x} \log ^2(2)}{x}-2 \text {Ei}(x) \log ^2(2)-2 \int e^x \, dx+4 \int e^{2 x} x^3 \, dx+6 \int e^{2 x} x^2 \, dx-10 \int e^x x^4 \, dx-64 \int e^x x^3 \, dx-72 \int e^x x^2 \, dx-\left (2 \log ^2(2)\right ) \int \frac {e^{2 x}}{x^2} \, dx-\left (4 \log ^2(2)\right ) \int \frac {e^x}{x} \, dx+\left (4 \log ^2(2)\right ) \int \frac {e^{2 x}}{x} \, dx+\left (6 \log ^2(2)\right ) \int \frac {e^x}{x^2} \, dx\\ &=6 e^x-e^{2 x}-6 x+2 e^x x-x^2-72 e^x x^2+3 e^{2 x} x^2-40 e^x x^3-9 x^4+6 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-\frac {2 e^x \log ^2(2)}{x}-6 \text {Ei}(x) \log ^2(2)+4 \text {Ei}(2 x) \log ^2(2)-6 \int e^{2 x} x \, dx-6 \int e^{2 x} x^2 \, dx+40 \int e^x x^3 \, dx+144 \int e^x x \, dx+192 \int e^x x^2 \, dx-\left (4 \log ^2(2)\right ) \int \frac {e^{2 x}}{x} \, dx+\left (6 \log ^2(2)\right ) \int \frac {e^x}{x} \, dx\\ &=6 e^x-e^{2 x}-6 x+146 e^x x-3 e^{2 x} x-x^2+120 e^x x^2-9 x^4+6 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-\frac {2 e^x \log ^2(2)}{x}+3 \int e^{2 x} \, dx+6 \int e^{2 x} x \, dx-120 \int e^x x^2 \, dx-144 \int e^x \, dx-384 \int e^x x \, dx\\ &=-138 e^x+\frac {e^{2 x}}{2}-6 x-238 e^x x-x^2-9 x^4+6 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-\frac {2 e^x \log ^2(2)}{x}-3 \int e^{2 x} \, dx+240 \int e^x x \, dx+384 \int e^x \, dx\\ &=246 e^x-e^{2 x}-6 x+2 e^x x-x^2-9 x^4+6 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-\frac {2 e^x \log ^2(2)}{x}-240 \int e^x \, dx\\ &=6 e^x-e^{2 x}-6 x+2 e^x x-x^2-9 x^4+6 e^x x^4-e^{2 x} x^4-6 x^5+2 e^x x^5-x^6+\frac {9 \log ^2(2)}{x^2}-\frac {6 e^x \log ^2(2)}{x^2}+\frac {e^{2 x} \log ^2(2)}{x^2}+\frac {6 \log ^2(2)}{x}-\frac {2 e^x \log ^2(2)}{x}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.63, size = 80, normalized size = 2.35 \begin {gather*} -\frac {6 x^3+x^4+9 x^6+6 x^7+x^8-9 \log ^2(2)-6 x \log ^2(2)+e^{2 x} \left (x^2+x^6-\log ^2(2)\right )-2 e^x (3+x) \left (x^2+x^6-\log ^2(2)\right )}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*x^3 - 2*x^4 - 36*x^6 - 30*x^7 - 6*x^8 + (-18 - 6*x)*Log[2]^2 + E^(2*x)*(-2*x^3 - 4*x^6 - 2*x^7 +
(-2 + 2*x)*Log[2]^2) + E^x*(8*x^3 + 2*x^4 + 24*x^6 + 16*x^7 + 2*x^8 + (12 - 4*x - 2*x^2)*Log[2]^2))/x^3,x]

[Out]

-((6*x^3 + x^4 + 9*x^6 + 6*x^7 + x^8 - 9*Log[2]^2 - 6*x*Log[2]^2 + E^(2*x)*(x^2 + x^6 - Log[2]^2) - 2*E^x*(3 +
x)*(x^2 + x^6 - Log[2]^2))/x^2)

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fricas [B]  time = 0.57, size = 86, normalized size = 2.53 \begin {gather*} -\frac {x^{8} + 6 \, x^{7} + 9 \, x^{6} + x^{4} + 6 \, x^{3} - 3 \, {\left (2 \, x + 3\right )} \log \relax (2)^{2} + {\left (x^{6} + x^{2} - \log \relax (2)^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{7} + 3 \, x^{6} + x^{3} - {\left (x + 3\right )} \log \relax (2)^{2} + 3 \, x^{2}\right )} e^{x}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x-2)*log(2)^2-2*x^7-4*x^6-2*x^3)*exp(x)^2+((-2*x^2-4*x+12)*log(2)^2+2*x^8+16*x^7+24*x^6+2*x^4+8
*x^3)*exp(x)+(-6*x-18)*log(2)^2-6*x^8-30*x^7-36*x^6-2*x^4-6*x^3)/x^3,x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.24, size = 111, normalized size = 3.26 \begin {gather*} -\frac {x^{8} - 2 \, x^{7} e^{x} + 6 \, x^{7} + x^{6} e^{\left (2 \, x\right )} - 6 \, x^{6} e^{x} + 9 \, x^{6} + x^{4} - 2 \, x^{3} e^{x} + 2 \, x e^{x} \log \relax (2)^{2} + 6 \, x^{3} + x^{2} e^{\left (2 \, x\right )} - 6 \, x^{2} e^{x} - 6 \, x \log \relax (2)^{2} - e^{\left (2 \, x\right )} \log \relax (2)^{2} + 6 \, e^{x} \log \relax (2)^{2} - 9 \, \log \relax (2)^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x-2)*log(2)^2-2*x^7-4*x^6-2*x^3)*exp(x)^2+((-2*x^2-4*x+12)*log(2)^2+2*x^8+16*x^7+24*x^6+2*x^4+8
*x^3)*exp(x)+(-6*x-18)*log(2)^2-6*x^8-30*x^7-36*x^6-2*x^4-6*x^3)/x^3,x, algorithm="giac")

[Out]

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

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maple [B]  time = 0.16, size = 106, normalized size = 3.12

method	result	size
risch	\(-x^{6}-6 x^{5}-9 x^{4}-x^{2}-6 x +\frac {6 x \ln \relax (2)^{2}+9 \ln \relax (2)^{2}}{x^{2}}+\frac {\left (\ln \relax (2)^{2}-x^{2}-x^{6}\right ) {\mathrm e}^{2 x}}{x^{2}}-\frac {2 \left (-x^{7}-3 x^{6}+x \ln \relax (2)^{2}-x^{3}+3 \ln \relax (2)^{2}-3 x^{2}\right ) {\mathrm e}^{x}}{x^{2}}\)	\(106\)
default	\(-x^{6}-6 x^{5}-9 x^{4}-x^{2}-6 x -{\mathrm e}^{2 x}+\frac {9 \ln \relax (2)^{2}}{x^{2}}+2 x^{5} {\mathrm e}^{x}+6 \,{\mathrm e}^{x} x^{4}+2 \,{\mathrm e}^{x} x +6 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} x^{4}+\frac {6 \ln \relax (2)^{2}}{x}-\frac {6 \ln \relax (2)^{2} {\mathrm e}^{x}}{x^{2}}-\frac {2 \ln \relax (2)^{2} {\mathrm e}^{x}}{x}+\frac {\ln \relax (2)^{2} {\mathrm e}^{2 x}}{x^{2}}\)	\(115\)
norman	\(\frac {\ln \relax (2)^{2} {\mathrm e}^{2 x}-6 x^{3}-x^{4}-9 x^{6}-6 x^{7}-x^{8}+9 \ln \relax (2)^{2}+6 x \ln \relax (2)^{2}+6 x^{6} {\mathrm e}^{x}-{\mathrm e}^{2 x} x^{6}+2 x^{7} {\mathrm e}^{x}+6 \,{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{x} x^{3}-{\mathrm e}^{2 x} x^{2}-6 \ln \relax (2)^{2} {\mathrm e}^{x}-2 x \ln \relax (2)^{2} {\mathrm e}^{x}}{x^{2}}\)	\(116\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x-2)*ln(2)^2-2*x^7-4*x^6-2*x^3)*exp(x)^2+((-2*x^2-4*x+12)*ln(2)^2+2*x^8+16*x^7+24*x^6+2*x^4+8*x^3)*ex
p(x)+(-6*x-18)*ln(2)^2-6*x^8-30*x^7-36*x^6-2*x^4-6*x^3)/x^3,x,method=_RETURNVERBOSE)

[Out]

-x^6-6*x^5-9*x^4-x^2-6*x+(6*x*ln(2)^2+9*ln(2)^2)/x^2+(ln(2)^2-x^2-x^6)/x^2*exp(2*x)-2*(-x^7-3*x^6+x*ln(2)^2-x^
3+3*ln(2)^2-3*x^2)/x^2*exp(x)

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maxima [C]  time = 0.41, size = 224, normalized size = 6.59 \begin {gather*} -x^{6} - 6 \, x^{5} - 9 \, x^{4} - 2 \, {\rm Ei}\relax (x) \log \relax (2)^{2} - 4 \, \Gamma \left (-1, -x\right ) \log \relax (2)^{2} + 4 \, \Gamma \left (-1, -2 \, x\right ) \log \relax (2)^{2} - 12 \, \Gamma \left (-2, -x\right ) \log \relax (2)^{2} + 8 \, \Gamma \left (-2, -2 \, x\right ) \log \relax (2)^{2} - x^{2} - \frac {1}{2} \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x\right )} - \frac {1}{2} \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - 5 \, x^{4} + 20 \, x^{3} - 60 \, x^{2} + 120 \, x - 120\right )} e^{x} + 16 \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} + 24 \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + 2 \, {\left (x - 1\right )} e^{x} - 6 \, x + \frac {6 \, \log \relax (2)^{2}}{x} + \frac {9 \, \log \relax (2)^{2}}{x^{2}} - e^{\left (2 \, x\right )} + 8 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x-2)*log(2)^2-2*x^7-4*x^6-2*x^3)*exp(x)^2+((-2*x^2-4*x+12)*log(2)^2+2*x^8+16*x^7+24*x^6+2*x^4+8
*x^3)*exp(x)+(-6*x-18)*log(2)^2-6*x^8-30*x^7-36*x^6-2*x^4-6*x^3)/x^3,x, algorithm="maxima")

[Out]

-x^6 - 6*x^5 - 9*x^4 - 2*Ei(x)*log(2)^2 - 4*gamma(-1, -x)*log(2)^2 + 4*gamma(-1, -2*x)*log(2)^2 - 12*gamma(-2,
-x)*log(2)^2 + 8*gamma(-2, -2*x)*log(2)^2 - x^2 - 1/2*(2*x^4 - 4*x^3 + 6*x^2 - 6*x + 3)*e^(2*x) - 1/2*(4*x^3
- 6*x^2 + 6*x - 3)*e^(2*x) + 2*(x^5 - 5*x^4 + 20*x^3 - 60*x^2 + 120*x - 120)*e^x + 16*(x^4 - 4*x^3 + 12*x^2 -
24*x + 24)*e^x + 24*(x^3 - 3*x^2 + 6*x - 6)*e^x + 2*(x - 1)*e^x - 6*x + 6*log(2)^2/x + 9*log(2)^2/x^2 - e^(2*x
) + 8*e^x

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mupad [B]  time = 0.20, size = 101, normalized size = 2.97 \begin {gather*} 6\,{\mathrm {e}}^x-{\mathrm {e}}^{2\,x}-x^4\,\left ({\mathrm {e}}^{2\,x}-6\,{\mathrm {e}}^x+9\right )+x\,\left (2\,{\mathrm {e}}^x-6\right )-\frac {6\,{\mathrm {e}}^x\,{\ln \relax (2)}^2-{\mathrm {e}}^{2\,x}\,{\ln \relax (2)}^2+x\,\left (2\,{\mathrm {e}}^x\,{\ln \relax (2)}^2-6\,{\ln \relax (2)}^2\right )-9\,{\ln \relax (2)}^2}{x^2}+x^5\,\left (2\,{\mathrm {e}}^x-6\right )-x^2-x^6 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*x)*(2*x^3 - log(2)^2*(2*x - 2) + 4*x^6 + 2*x^7) - exp(x)*(8*x^3 - log(2)^2*(4*x + 2*x^2 - 12) + 2*
x^4 + 24*x^6 + 16*x^7 + 2*x^8) + log(2)^2*(6*x + 18) + 6*x^3 + 2*x^4 + 36*x^6 + 30*x^7 + 6*x^8)/x^3,x)

[Out]

6*exp(x) - exp(2*x) - x^4*(exp(2*x) - 6*exp(x) + 9) + x*(2*exp(x) - 6) - (6*exp(x)*log(2)^2 - exp(2*x)*log(2)^
2 + x*(2*exp(x)*log(2)^2 - 6*log(2)^2) - 9*log(2)^2)/x^2 + x^5*(2*exp(x) - 6) - x^2 - x^6

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sympy [B]  time = 0.31, size = 107, normalized size = 3.15 \begin {gather*} - x^{6} - 6 x^{5} - 9 x^{4} - x^{2} - 6 x - \frac {- 6 x \log {\relax (2 )}^{2} - 9 \log {\relax (2 )}^{2}}{x^{2}} + \frac {\left (- x^{8} - x^{4} + x^{2} \log {\relax (2 )}^{2}\right ) e^{2 x} + \left (2 x^{9} + 6 x^{8} + 2 x^{5} + 6 x^{4} - 2 x^{3} \log {\relax (2 )}^{2} - 6 x^{2} \log {\relax (2 )}^{2}\right ) e^{x}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x-2)*ln(2)**2-2*x**7-4*x**6-2*x**3)*exp(x)**2+((-2*x**2-4*x+12)*ln(2)**2+2*x**8+16*x**7+24*x**6
+2*x**4+8*x**3)*exp(x)+(-6*x-18)*ln(2)**2-6*x**8-30*x**7-36*x**6-2*x**4-6*x**3)/x**3,x)

[Out]

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

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