3.49.85 \(\int \frac {-32 e x^5+32 x^6+e^{8 x^2} (-32 x^2+256 x^4+e^2 (-64+256 x^2)+e (96 x-512 x^3))+e^{6 x^2} (64 x^3-768 x^5+e^2 (192 x-768 x^3)+e (-256 x^2+1536 x^4))+e^{4 x^2} (768 x^6+e^2 (-192 x^2+768 x^4)+e (192 x^3-1536 x^5))+e^{2 x^2} (-64 x^5+512 e x^6-256 x^7+e^2 (64 x^3-256 x^5))}{x^5} \, dx\) [4885]

Optimal. Leaf size=25 \[ \frac {16 (e-x)^2 \left (-e^{2 x^2}+x\right )^4}{x^4} \]

[Out]

16*(exp(1)-x)^2/x^4*(x-exp(x^2)^2)^4

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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(122\) vs. \(2(25)=50\).
time = 0.45, antiderivative size = 122, normalized size of antiderivative = 4.88, number of steps used = 6, number of rules used = 2, integrand size = 184, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {14, 2326} \begin {gather*} -\frac {64 e^{2 x^2} \left (e x^2-x^3\right ) (e-x)}{x^3}+\frac {16 e^{8 x^2} \left (e x^2-x^3\right ) (e-x)}{x^6}-\frac {64 e^{6 x^2} \left (e x^2-x^3\right ) (e-x)}{x^5}+\frac {96 e^{4 x^2} \left (e x^2-x^3\right ) (e-x)}{x^4}+16 (e-x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-32*E*x^5 + 32*x^6 + E^(8*x^2)*(-32*x^2 + 256*x^4 + E^2*(-64 + 256*x^2) + E*(96*x - 512*x^3)) + E^(6*x^2)
*(64*x^3 - 768*x^5 + E^2*(192*x - 768*x^3) + E*(-256*x^2 + 1536*x^4)) + E^(4*x^2)*(768*x^6 + E^2*(-192*x^2 + 7
68*x^4) + E*(192*x^3 - 1536*x^5)) + E^(2*x^2)*(-64*x^5 + 512*E*x^6 - 256*x^7 + E^2*(64*x^3 - 256*x^5)))/x^5,x]

[Out]

16*(E - x)^2 + (16*E^(8*x^2)*(E - x)*(E*x^2 - x^3))/x^6 - (64*E^(6*x^2)*(E - x)*(E*x^2 - x^3))/x^5 + (96*E^(4*
x^2)*(E - x)*(E*x^2 - x^3))/x^4 - (64*E^(2*x^2)*(E - x)*(E*x^2 - x^3))/x^3

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 2326

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-32 (e-x)-\frac {64 e^{6 x^2} (e-x) \left (-3 e+x+12 e x^2-12 x^3\right )}{x^4}+\frac {32 e^{8 x^2} (e-x) \left (-2 e+x+8 e x^2-8 x^3\right )}{x^5}+\frac {192 e^{4 x^2} (e-x) \left (-e+4 e x^2-4 x^3\right )}{x^3}-\frac {64 e^{2 x^2} (e-x) \left (-e-x+4 e x^2-4 x^3\right )}{x^2}\right ) \, dx\\ &=16 (e-x)^2+32 \int \frac {e^{8 x^2} (e-x) \left (-2 e+x+8 e x^2-8 x^3\right )}{x^5} \, dx-64 \int \frac {e^{6 x^2} (e-x) \left (-3 e+x+12 e x^2-12 x^3\right )}{x^4} \, dx-64 \int \frac {e^{2 x^2} (e-x) \left (-e-x+4 e x^2-4 x^3\right )}{x^2} \, dx+192 \int \frac {e^{4 x^2} (e-x) \left (-e+4 e x^2-4 x^3\right )}{x^3} \, dx\\ &=16 (e-x)^2+\frac {16 e^{8 x^2} (e-x) \left (e x^2-x^3\right )}{x^6}-\frac {64 e^{6 x^2} (e-x) \left (e x^2-x^3\right )}{x^5}+\frac {96 e^{4 x^2} (e-x) \left (e x^2-x^3\right )}{x^4}-\frac {64 e^{2 x^2} (e-x) \left (e x^2-x^3\right )}{x^3}\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(25)=50\).
time = 10.34, size = 85, normalized size = 3.40 \begin {gather*} \frac {16 \left (e^{8 x^2} (e-x)^2-4 e^{6 x^2} (e-x)^2 x+6 e^{4 x^2} (e-x)^2 x^2-4 e^{2 x^2} (e-x)^2 x^3-2 e x^5+x^6\right )}{x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-32*E*x^5 + 32*x^6 + E^(8*x^2)*(-32*x^2 + 256*x^4 + E^2*(-64 + 256*x^2) + E*(96*x - 512*x^3)) + E^(
6*x^2)*(64*x^3 - 768*x^5 + E^2*(192*x - 768*x^3) + E*(-256*x^2 + 1536*x^4)) + E^(4*x^2)*(768*x^6 + E^2*(-192*x
^2 + 768*x^4) + E*(192*x^3 - 1536*x^5)) + E^(2*x^2)*(-64*x^5 + 512*E*x^6 - 256*x^7 + E^2*(64*x^3 - 256*x^5)))/
x^5,x]

[Out]

(16*(E^(8*x^2)*(E - x)^2 - 4*E^(6*x^2)*(E - x)^2*x + 6*E^(4*x^2)*(E - x)^2*x^2 - 4*E^(2*x^2)*(E - x)^2*x^3 - 2
*E*x^5 + x^6))/x^4

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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.49, size = 434, normalized size = 17.36

method	result	size
risch	\(-32 x \,{\mathrm e}+16 x^{2}+\frac {16 \left (-2 x \,{\mathrm e}+x^{2}+{\mathrm e}^{2}\right ) {\mathrm e}^{8 x^{2}}}{x^{4}}-\frac {64 \left (-2 x \,{\mathrm e}+x^{2}+{\mathrm e}^{2}\right ) {\mathrm e}^{6 x^{2}}}{x^{3}}+\frac {96 \left (-2 x \,{\mathrm e}+x^{2}+{\mathrm e}^{2}\right ) {\mathrm e}^{4 x^{2}}}{x^{2}}-\frac {64 \left (-2 x \,{\mathrm e}+x^{2}+{\mathrm e}^{2}\right ) {\mathrm e}^{2 x^{2}}}{x}\)	\(100\)
default	\(16 x^{2}+\frac {16 \,{\mathrm e}^{8 x^{2}}}{x^{2}}-\frac {64 \,{\mathrm e}^{6 x^{2}}}{x}+96 \,{\mathrm e}^{4 x^{2}}-64 x \,{\mathrm e}^{2 x^{2}}-384 \,{\mathrm e} \sqrt {\pi }\, \erfi \left (2 x \right )-64 \,{\mathrm e}^{2} \sqrt {2}\, \sqrt {\pi }\, \erfi \left (\sqrt {2}\, x \right )-64 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{8 x^{2}}}{4 x^{4}}-\frac {2 \,{\mathrm e}^{8 x^{2}}}{x^{2}}-16 \expIntegral \left (1, -8 x^{2}\right )\right )+96 \,{\mathrm e} \left (-\frac {{\mathrm e}^{8 x^{2}}}{3 x^{3}}-\frac {16 \,{\mathrm e}^{8 x^{2}}}{3 x}+\frac {32 \sqrt {2}\, \sqrt {\pi }\, \erfi \left (2 \sqrt {2}\, x \right )}{3}\right )+192 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{6 x^{2}}}{3 x^{3}}-\frac {4 \,{\mathrm e}^{6 x^{2}}}{x}+4 \sqrt {6}\, \sqrt {\pi }\, \erfi \left (\sqrt {6}\, x \right )\right )-256 \,{\mathrm e} \left (-\frac {{\mathrm e}^{6 x^{2}}}{2 x^{2}}-3 \expIntegral \left (1, -6 x^{2}\right )\right )-192 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{4 x^{2}}}{2 x^{2}}-2 \expIntegral \left (1, -4 x^{2}\right )\right )+256 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{8 x^{2}}}{2 x^{2}}-4 \expIntegral \left (1, -8 x^{2}\right )\right )+192 \,{\mathrm e} \left (-\frac {{\mathrm e}^{4 x^{2}}}{x}+2 \sqrt {\pi }\, \erfi \left (2 x \right )\right )-512 \,{\mathrm e} \left (-\frac {{\mathrm e}^{8 x^{2}}}{x}+2 \sqrt {2}\, \sqrt {\pi }\, \erfi \left (2 \sqrt {2}\, x \right )\right )+64 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{2 x^{2}}}{x}+\sqrt {2}\, \sqrt {\pi }\, \erfi \left (\sqrt {2}\, x \right )\right )-768 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{6 x^{2}}}{x}+\sqrt {6}\, \sqrt {\pi }\, \erfi \left (\sqrt {6}\, x \right )\right )-768 \,{\mathrm e} \expIntegral \left (1, -6 x^{2}\right )-384 \,{\mathrm e}^{2} \expIntegral \left (1, -4 x^{2}\right )+128 \,{\mathrm e} \,{\mathrm e}^{2 x^{2}}-32 x \,{\mathrm e}\)	\(434\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((256*x^2-64)*exp(1)^2+(-512*x^3+96*x)*exp(1)+256*x^4-32*x^2)*exp(x^2)^8+((-768*x^3+192*x)*exp(1)^2+(1536
*x^4-256*x^2)*exp(1)-768*x^5+64*x^3)*exp(x^2)^6+((768*x^4-192*x^2)*exp(1)^2+(-1536*x^5+192*x^3)*exp(1)+768*x^6
)*exp(x^2)^4+((-256*x^5+64*x^3)*exp(1)^2+512*x^6*exp(1)-256*x^7-64*x^5)*exp(x^2)^2-32*x^5*exp(1)+32*x^6)/x^5,x
,method=_RETURNVERBOSE)

[Out]

16*x^2+16*exp(x^2)^8/x^2-64*exp(x^2)^6/x+96*exp(x^2)^4-64*x*exp(x^2)^2-384*exp(1)*Pi^(1/2)*erfi(2*x)-64*exp(1)
^2*2^(1/2)*Pi^(1/2)*erfi(2^(1/2)*x)-64*exp(1)^2*(-1/4/x^4*exp(x^2)^8-2*exp(x^2)^8/x^2-16*Ei(1,-8*x^2))+96*exp(
1)*(-1/3/x^3*exp(x^2)^8-16/3/x*exp(x^2)^8+32/3*2^(1/2)*Pi^(1/2)*erfi(2*2^(1/2)*x))+192*exp(1)^2*(-1/3/x^3*exp(
x^2)^6-4*exp(x^2)^6/x+4*6^(1/2)*Pi^(1/2)*erfi(6^(1/2)*x))-256*exp(1)*(-1/2/x^2*exp(x^2)^6-3*Ei(1,-6*x^2))-192*
exp(1)^2*(-1/2*exp(x^2)^4/x^2-2*Ei(1,-4*x^2))+256*exp(1)^2*(-1/2*exp(x^2)^8/x^2-4*Ei(1,-8*x^2))+192*exp(1)*(-e
xp(x^2)^4/x+2*Pi^(1/2)*erfi(2*x))-512*exp(1)*(-1/x*exp(x^2)^8+2*2^(1/2)*Pi^(1/2)*erfi(2*2^(1/2)*x))+64*exp(1)^
2*(-exp(x^2)^2/x+2^(1/2)*Pi^(1/2)*erfi(2^(1/2)*x))-768*exp(1)^2*(-exp(x^2)^6/x+6^(1/2)*Pi^(1/2)*erfi(6^(1/2)*x
))-768*exp(1)*Ei(1,-6*x^2)-384*exp(1)^2*Ei(1,-4*x^2)+128*exp(1)*exp(x^2)^2-32*x*exp(1)

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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.60, size = 325, normalized size = 13.00 \begin {gather*} 64 i \, \sqrt {2} \sqrt {\pi } \operatorname {erf}\left (i \, \sqrt {2} x\right ) e^{2} + 384 i \, \sqrt {\pi } \operatorname {erf}\left (2 i \, x\right ) e + 16 \, x^{2} + 64 i \, \sqrt {6} \sqrt {\pi } \operatorname {erf}\left (i \, \sqrt {6} x\right ) + 384 \, {\rm Ei}\left (4 \, x^{2}\right ) e^{2} - 32 \, x e + 768 \, {\rm Ei}\left (6 \, x^{2}\right ) e - 64 \, x e^{\left (2 \, x^{2}\right )} - \frac {32 \, \sqrt {2} \sqrt {-x^{2}} e^{2} \Gamma \left (-\frac {1}{2}, -2 \, x^{2}\right )}{x} + \frac {384 \, \sqrt {6} \sqrt {-x^{2}} e^{2} \Gamma \left (-\frac {1}{2}, -6 \, x^{2}\right )}{x} + \frac {512 \, \sqrt {2} \sqrt {-x^{2}} e \Gamma \left (-\frac {1}{2}, -8 \, x^{2}\right )}{x} - 384 \, e^{2} \Gamma \left (-1, -4 \, x^{2}\right ) - 768 \, e \Gamma \left (-1, -6 \, x^{2}\right ) + 1024 \, e^{2} \Gamma \left (-1, -8 \, x^{2}\right ) + 2048 \, e^{2} \Gamma \left (-2, -8 \, x^{2}\right ) - \frac {192 \, \sqrt {-x^{2}} e \Gamma \left (-\frac {1}{2}, -4 \, x^{2}\right )}{x} - \frac {32 \, \sqrt {6} \sqrt {-x^{2}} \Gamma \left (-\frac {1}{2}, -6 \, x^{2}\right )}{x} - \frac {576 \, \sqrt {6} \left (-x^{2}\right )^{\frac {3}{2}} e^{2} \Gamma \left (-\frac {3}{2}, -6 \, x^{2}\right )}{x^{3}} - \frac {768 \, \sqrt {2} \left (-x^{2}\right )^{\frac {3}{2}} e \Gamma \left (-\frac {3}{2}, -8 \, x^{2}\right )}{x^{3}} + 128 \, {\rm Ei}\left (8 \, x^{2}\right ) + 96 \, e^{\left (4 \, x^{2}\right )} + 128 \, e^{\left (2 \, x^{2} + 1\right )} - 128 \, \Gamma \left (-1, -8 \, x^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^2-64)*exp(1)^2+(-512*x^3+96*x)*exp(1)+256*x^4-32*x^2)*exp(x^2)^8+((-768*x^3+192*x)*exp(1)^2
+(1536*x^4-256*x^2)*exp(1)-768*x^5+64*x^3)*exp(x^2)^6+((768*x^4-192*x^2)*exp(1)^2+(-1536*x^5+192*x^3)*exp(1)+7
68*x^6)*exp(x^2)^4+((-256*x^5+64*x^3)*exp(1)^2+512*x^6*exp(1)-256*x^7-64*x^5)*exp(x^2)^2-32*x^5*exp(1)+32*x^6)
/x^5,x, algorithm="maxima")

[Out]

64*I*sqrt(2)*sqrt(pi)*erf(I*sqrt(2)*x)*e^2 + 384*I*sqrt(pi)*erf(2*I*x)*e + 16*x^2 + 64*I*sqrt(6)*sqrt(pi)*erf(
I*sqrt(6)*x) + 384*Ei(4*x^2)*e^2 - 32*x*e + 768*Ei(6*x^2)*e - 64*x*e^(2*x^2) - 32*sqrt(2)*sqrt(-x^2)*e^2*gamma
(-1/2, -2*x^2)/x + 384*sqrt(6)*sqrt(-x^2)*e^2*gamma(-1/2, -6*x^2)/x + 512*sqrt(2)*sqrt(-x^2)*e*gamma(-1/2, -8*
x^2)/x - 384*e^2*gamma(-1, -4*x^2) - 768*e*gamma(-1, -6*x^2) + 1024*e^2*gamma(-1, -8*x^2) + 2048*e^2*gamma(-2,
-8*x^2) - 192*sqrt(-x^2)*e*gamma(-1/2, -4*x^2)/x - 32*sqrt(6)*sqrt(-x^2)*gamma(-1/2, -6*x^2)/x - 576*sqrt(6)*
(-x^2)^(3/2)*e^2*gamma(-3/2, -6*x^2)/x^3 - 768*sqrt(2)*(-x^2)^(3/2)*e*gamma(-3/2, -8*x^2)/x^3 + 128*Ei(8*x^2)
+ 96*e^(4*x^2) + 128*e^(2*x^2 + 1) - 128*gamma(-1, -8*x^2)

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (25) = 50\).
time = 0.40, size = 107, normalized size = 4.28 \begin {gather*} \frac {16 \, {\left (x^{6} - 2 \, x^{5} e + {\left (x^{2} - 2 \, x e + e^{2}\right )} e^{\left (8 \, x^{2}\right )} - 4 \, {\left (x^{3} - 2 \, x^{2} e + x e^{2}\right )} e^{\left (6 \, x^{2}\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} e + x^{2} e^{2}\right )} e^{\left (4 \, x^{2}\right )} - 4 \, {\left (x^{5} - 2 \, x^{4} e + x^{3} e^{2}\right )} e^{\left (2 \, x^{2}\right )}\right )}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^2-64)*exp(1)^2+(-512*x^3+96*x)*exp(1)+256*x^4-32*x^2)*exp(x^2)^8+((-768*x^3+192*x)*exp(1)^2
+(1536*x^4-256*x^2)*exp(1)-768*x^5+64*x^3)*exp(x^2)^6+((768*x^4-192*x^2)*exp(1)^2+(-1536*x^5+192*x^3)*exp(1)+7
68*x^6)*exp(x^2)^4+((-256*x^5+64*x^3)*exp(1)^2+512*x^6*exp(1)-256*x^7-64*x^5)*exp(x^2)^2-32*x^5*exp(1)+32*x^6)
/x^5,x, algorithm="fricas")

[Out]

16*(x^6 - 2*x^5*e + (x^2 - 2*x*e + e^2)*e^(8*x^2) - 4*(x^3 - 2*x^2*e + x*e^2)*e^(6*x^2) + 6*(x^4 - 2*x^3*e + x
^2*e^2)*e^(4*x^2) - 4*(x^5 - 2*x^4*e + x^3*e^2)*e^(2*x^2))/x^4

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (20) = 40\).
time = 0.18, size = 129, normalized size = 5.16 \begin {gather*} 16 x^{2} - 32 e x + \frac {\left (16 x^{8} - 32 e x^{7} + 16 x^{6} e^{2}\right ) e^{8 x^{2}} + \left (- 64 x^{9} + 128 e x^{8} - 64 x^{7} e^{2}\right ) e^{6 x^{2}} + \left (96 x^{10} - 192 e x^{9} + 96 x^{8} e^{2}\right ) e^{4 x^{2}} + \left (- 64 x^{11} + 128 e x^{10} - 64 x^{9} e^{2}\right ) e^{2 x^{2}}}{x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x**2-64)*exp(1)**2+(-512*x**3+96*x)*exp(1)+256*x**4-32*x**2)*exp(x**2)**8+((-768*x**3+192*x)*
exp(1)**2+(1536*x**4-256*x**2)*exp(1)-768*x**5+64*x**3)*exp(x**2)**6+((768*x**4-192*x**2)*exp(1)**2+(-1536*x**
5+192*x**3)*exp(1)+768*x**6)*exp(x**2)**4+((-256*x**5+64*x**3)*exp(1)**2+512*x**6*exp(1)-256*x**7-64*x**5)*exp
(x**2)**2-32*x**5*exp(1)+32*x**6)/x**5,x)

[Out]

16*x**2 - 32*E*x + ((16*x**8 - 32*E*x**7 + 16*x**6*exp(2))*exp(8*x**2) + (-64*x**9 + 128*E*x**8 - 64*x**7*exp(
2))*exp(6*x**2) + (96*x**10 - 192*E*x**9 + 96*x**8*exp(2))*exp(4*x**2) + (-64*x**11 + 128*E*x**10 - 64*x**9*ex
p(2))*exp(2*x**2))/x**10

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (25) = 50\).
time = 0.44, size = 154, normalized size = 6.16 \begin {gather*} \frac {16 \, {\left (x^{6} - 2 \, x^{5} e - 4 \, x^{5} e^{\left (2 \, x^{2}\right )} + 6 \, x^{4} e^{\left (4 \, x^{2}\right )} + 8 \, x^{4} e^{\left (2 \, x^{2} + 1\right )} - 4 \, x^{3} e^{\left (6 \, x^{2}\right )} - 12 \, x^{3} e^{\left (4 \, x^{2} + 1\right )} - 4 \, x^{3} e^{\left (2 \, x^{2} + 2\right )} + x^{2} e^{\left (8 \, x^{2}\right )} + 8 \, x^{2} e^{\left (6 \, x^{2} + 1\right )} + 6 \, x^{2} e^{\left (4 \, x^{2} + 2\right )} - 2 \, x e^{\left (8 \, x^{2} + 1\right )} - 4 \, x e^{\left (6 \, x^{2} + 2\right )} + e^{\left (8 \, x^{2} + 2\right )}\right )}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((256*x^2-64)*exp(1)^2+(-512*x^3+96*x)*exp(1)+256*x^4-32*x^2)*exp(x^2)^8+((-768*x^3+192*x)*exp(1)^2
+(1536*x^4-256*x^2)*exp(1)-768*x^5+64*x^3)*exp(x^2)^6+((768*x^4-192*x^2)*exp(1)^2+(-1536*x^5+192*x^3)*exp(1)+7
68*x^6)*exp(x^2)^4+((-256*x^5+64*x^3)*exp(1)^2+512*x^6*exp(1)-256*x^7-64*x^5)*exp(x^2)^2-32*x^5*exp(1)+32*x^6)
/x^5,x, algorithm="giac")

[Out]

16*(x^6 - 2*x^5*e - 4*x^5*e^(2*x^2) + 6*x^4*e^(4*x^2) + 8*x^4*e^(2*x^2 + 1) - 4*x^3*e^(6*x^2) - 12*x^3*e^(4*x^
2 + 1) - 4*x^3*e^(2*x^2 + 2) + x^2*e^(8*x^2) + 8*x^2*e^(6*x^2 + 1) + 6*x^2*e^(4*x^2 + 2) - 2*x*e^(8*x^2 + 1) -
4*x*e^(6*x^2 + 2) + e^(8*x^2 + 2))/x^4

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Mupad [B]
time = 3.47, size = 151, normalized size = 6.04 \begin {gather*} 96\,{\mathrm {e}}^{4\,x^2}-32\,x\,\mathrm {e}+128\,\mathrm {e}\,{\mathrm {e}}^{2\,x^2}-64\,x\,{\mathrm {e}}^{2\,x^2}-\frac {64\,{\mathrm {e}}^{6\,x^2}}{x}+\frac {16\,{\mathrm {e}}^{8\,x^2}}{x^2}+16\,x^2-\frac {64\,{\mathrm {e}}^2\,{\mathrm {e}}^{2\,x^2}}{x}-\frac {192\,\mathrm {e}\,{\mathrm {e}}^{4\,x^2}}{x}+\frac {96\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^2}}{x^2}+\frac {128\,\mathrm {e}\,{\mathrm {e}}^{6\,x^2}}{x^2}-\frac {64\,{\mathrm {e}}^2\,{\mathrm {e}}^{6\,x^2}}{x^3}-\frac {32\,\mathrm {e}\,{\mathrm {e}}^{8\,x^2}}{x^3}+\frac {16\,{\mathrm {e}}^2\,{\mathrm {e}}^{8\,x^2}}{x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(8*x^2)*(exp(1)*(96*x - 512*x^3) + exp(2)*(256*x^2 - 64) - 32*x^2 + 256*x^4) + exp(6*x^2)*(exp(2)*(192
*x - 768*x^3) - exp(1)*(256*x^2 - 1536*x^4) + 64*x^3 - 768*x^5) - 32*x^5*exp(1) + exp(4*x^2)*(exp(1)*(192*x^3
- 1536*x^5) - exp(2)*(192*x^2 - 768*x^4) + 768*x^6) + 32*x^6 + exp(2*x^2)*(exp(2)*(64*x^3 - 256*x^5) + 512*x^6
*exp(1) - 64*x^5 - 256*x^7))/x^5,x)

[Out]

96*exp(4*x^2) - 32*x*exp(1) + 128*exp(1)*exp(2*x^2) - 64*x*exp(2*x^2) - (64*exp(6*x^2))/x + (16*exp(8*x^2))/x^
2 + 16*x^2 - (64*exp(2)*exp(2*x^2))/x - (192*exp(1)*exp(4*x^2))/x + (96*exp(2)*exp(4*x^2))/x^2 + (128*exp(1)*e
xp(6*x^2))/x^2 - (64*exp(2)*exp(6*x^2))/x^3 - (32*exp(1)*exp(8*x^2))/x^3 + (16*exp(2)*exp(8*x^2))/x^4

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