3.18.29 \(\int (2 x+e^{-602 x-160 x^2 \log (e^{-x} x)-10 x^3 \log ^2(e^{-x} x)} (-602-160 x+160 x^2+(-320 x-20 x^2+20 x^3) \log (e^{-x} x)-30 x^2 \log ^2(e^{-x} x))+e^{-301 x-80 x^2 \log (e^{-x} x)-5 x^3 \log ^2(e^{-x} x)} (-2+602 x+160 x^2-160 x^3+(320 x^2+20 x^3-20 x^4) \log (e^{-x} x)+30 x^3 \log ^2(e^{-x} x))) \, dx\)

Optimal. Leaf size=33 \[ \left (e^{-x+5 x \left (4-\left (8+x \log \left (e^{-x} x\right )\right )^2\right )}-x\right )^2 \]

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Rubi [B]  time = 2.73, antiderivative size = 208, normalized size of antiderivative = 6.30, number of steps used = 3, number of rules used = 2, integrand size = 177, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6706, 2288} \begin {gather*} x^2+\left (e^{-x} x\right )^{-160 x^2} e^{-10 x^3 \log ^2\left (e^{-x} x\right )-602 x}-\frac {2 \left (e^{-x} x\right )^{-80 x^2} e^{-5 x^3 \log ^2\left (e^{-x} x\right )-301 x} \left (-80 x^3+15 x^3 \log ^2\left (e^{-x} x\right )+80 x^2+10 \left (-x^4+x^3+16 x^2\right ) \log \left (e^{-x} x\right )+301 x\right )}{15 x^2 \log ^2\left (e^{-x} x\right )+10 e^x \left (e^{-x}-e^{-x} x\right ) x^2 \log \left (e^{-x} x\right )+80 e^x \left (e^{-x}-e^{-x} x\right ) x+160 x \log \left (e^{-x} x\right )+301} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x + E^(-602*x - 160*x^2*Log[x/E^x] - 10*x^3*Log[x/E^x]^2)*(-602 - 160*x + 160*x^2 + (-320*x - 20*x^2 + 2
0*x^3)*Log[x/E^x] - 30*x^2*Log[x/E^x]^2) + E^(-301*x - 80*x^2*Log[x/E^x] - 5*x^3*Log[x/E^x]^2)*(-2 + 602*x + 1
60*x^2 - 160*x^3 + (320*x^2 + 20*x^3 - 20*x^4)*Log[x/E^x] + 30*x^3*Log[x/E^x]^2),x]

[Out]

x^2 + E^(-602*x - 10*x^3*Log[x/E^x]^2)/(x/E^x)^(160*x^2) - (2*E^(-301*x - 5*x^3*Log[x/E^x]^2)*(301*x + 80*x^2
- 80*x^3 + 10*(16*x^2 + x^3 - x^4)*Log[x/E^x] + 15*x^3*Log[x/E^x]^2))/((x/E^x)^(80*x^2)*(301 + 80*E^x*x*(E^(-x
) - x/E^x) + 160*x*Log[x/E^x] + 10*E^x*x^2*(E^(-x) - x/E^x)*Log[x/E^x] + 15*x^2*Log[x/E^x]^2))

Rule 2288

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]

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2+\int \exp \left (-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )\right ) \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right ) \, dx+\int \exp \left (-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )\right ) \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right ) \, dx\\ &=x^2+e^{-602 x-10 x^3 \log ^2\left (e^{-x} x\right )} \left (e^{-x} x\right )^{-160 x^2}-\frac {2 e^{-301 x-5 x^3 \log ^2\left (e^{-x} x\right )} \left (e^{-x} x\right )^{-80 x^2} \left (301 x+80 x^2-80 x^3+10 \left (16 x^2+x^3-x^4\right ) \log \left (e^{-x} x\right )+15 x^3 \log ^2\left (e^{-x} x\right )\right )}{301+80 e^x x \left (e^{-x}-e^{-x} x\right )+160 x \log \left (e^{-x} x\right )+10 e^x x^2 \left (e^{-x}-e^{-x} x\right ) \log \left (e^{-x} x\right )+15 x^2 \log ^2\left (e^{-x} x\right )}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.41, size = 173, normalized size = 5.24 \begin {gather*} e^{-2 x \left (301+80 x^2+10 x^4+5 x^2 \log ^2\left (e^{-x} x\right )\right )} x^{20 x^4} \left (e^{-x} x\right )^{-20 x^2 \left (8+x^2\right )} \left (e^{10 x^3 \left (8+x \left (x-\log (x)+\log \left (e^{-x} x\right )\right )\right )}-e^{x \left (301+5 x^4+5 x^2 \log ^2(x)+80 x \left (x-\log (x)+\log \left (e^{-x} x\right )\right )+5 x^2 \left (x-\log (x)+\log \left (e^{-x} x\right )\right )^2\right )} x^{1+80 x^2+10 x^3 \left (-\log (x)+\log \left (e^{-x} x\right )\right )}\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x + E^(-602*x - 160*x^2*Log[x/E^x] - 10*x^3*Log[x/E^x]^2)*(-602 - 160*x + 160*x^2 + (-320*x - 20*x
^2 + 20*x^3)*Log[x/E^x] - 30*x^2*Log[x/E^x]^2) + E^(-301*x - 80*x^2*Log[x/E^x] - 5*x^3*Log[x/E^x]^2)*(-2 + 602
*x + 160*x^2 - 160*x^3 + (320*x^2 + 20*x^3 - 20*x^4)*Log[x/E^x] + 30*x^3*Log[x/E^x]^2),x]

[Out]

(x^(20*x^4)*(E^(10*x^3*(8 + x*(x - Log[x] + Log[x/E^x]))) - E^(x*(301 + 5*x^4 + 5*x^2*Log[x]^2 + 80*x*(x - Log
[x] + Log[x/E^x]) + 5*x^2*(x - Log[x] + Log[x/E^x])^2))*x^(1 + 80*x^2 + 10*x^3*(-Log[x] + Log[x/E^x])))^2)/(E^
(2*x*(301 + 80*x^2 + 10*x^4 + 5*x^2*Log[x/E^x]^2))*(x/E^x)^(20*x^2*(8 + x^2)))

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fricas [B]  time = 0.56, size = 69, normalized size = 2.09 \begin {gather*} x^{2} - 2 \, x e^{\left (-5 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 301 \, x\right )} + e^{\left (-10 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 160 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 602 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-30*x^2*log(x/exp(x))^2+(20*x^3-20*x^2-320*x)*log(x/exp(x))+160*x^2-160*x-602)*exp(-5*x^3*log(x/exp
(x))^2-80*x^2*log(x/exp(x))-301*x)^2+(30*x^3*log(x/exp(x))^2+(-20*x^4+20*x^3+320*x^2)*log(x/exp(x))-160*x^3+16
0*x^2+602*x-2)*exp(-5*x^3*log(x/exp(x))^2-80*x^2*log(x/exp(x))-301*x)+2*x,x, algorithm="fricas")

[Out]

x^2 - 2*x*e^(-5*x^3*log(x*e^(-x))^2 - 80*x^2*log(x*e^(-x)) - 301*x) + e^(-10*x^3*log(x*e^(-x))^2 - 160*x^2*log
(x*e^(-x)) - 602*x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 2 \, {\left (15 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{3} + 80 \, x^{2} - 10 \, {\left (x^{4} - x^{3} - 16 \, x^{2}\right )} \log \left (x e^{\left (-x\right )}\right ) + 301 \, x - 1\right )} e^{\left (-5 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 301 \, x\right )} - 2 \, {\left (15 \, x^{2} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} - 10 \, {\left (x^{3} - x^{2} - 16 \, x\right )} \log \left (x e^{\left (-x\right )}\right ) + 80 \, x + 301\right )} e^{\left (-10 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 160 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 602 \, x\right )} + 2 \, x\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-30*x^2*log(x/exp(x))^2+(20*x^3-20*x^2-320*x)*log(x/exp(x))+160*x^2-160*x-602)*exp(-5*x^3*log(x/exp
(x))^2-80*x^2*log(x/exp(x))-301*x)^2+(30*x^3*log(x/exp(x))^2+(-20*x^4+20*x^3+320*x^2)*log(x/exp(x))-160*x^3+16
0*x^2+602*x-2)*exp(-5*x^3*log(x/exp(x))^2-80*x^2*log(x/exp(x))-301*x)+2*x,x, algorithm="giac")

[Out]

integrate(2*(15*x^3*log(x*e^(-x))^2 - 80*x^3 + 80*x^2 - 10*(x^4 - x^3 - 16*x^2)*log(x*e^(-x)) + 301*x - 1)*e^(
-5*x^3*log(x*e^(-x))^2 - 80*x^2*log(x*e^(-x)) - 301*x) - 2*(15*x^2*log(x*e^(-x))^2 - 80*x^2 - 10*(x^3 - x^2 -
16*x)*log(x*e^(-x)) + 80*x + 301)*e^(-10*x^3*log(x*e^(-x))^2 - 160*x^2*log(x*e^(-x)) - 602*x) + 2*x, x)

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maple [C]  time = 0.31, size = 1157, normalized size = 35.06

method	result	size
risch	\(\left ({\mathrm e}^{x}\right )^{-10 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) x^{3}} x^{10 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) x^{3}} \left ({\mathrm e}^{x}\right )^{10 i \pi \,\mathrm {csgn}\left (i x \right ) x^{3}} \left ({\mathrm e}^{x}\right )^{10 i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}} x^{-10 i \pi \,\mathrm {csgn}\left (i x \right ) x^{3}} x^{-10 i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}} \left ({\mathrm e}^{x}\right )^{20 x^{3} \ln \relax (x )} \left ({\mathrm e}^{x}\right )^{-10 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right ) x^{3}} x^{10 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right ) x^{3}} \left ({\mathrm e}^{x}\right )^{160 x^{2}} x^{-160 x^{2}} {\mathrm e}^{-\frac {x \left (-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )^{2}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{5} \mathrm {csgn}\left (i x \right )-20 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right )+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{6}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{5} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2}-160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3}-160 i x \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right )+160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )+160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )+20 x^{2} \ln \relax (x )^{2}+20 x^{2} \ln \left ({\mathrm e}^{x}\right )^{2}+1204\right )}{2}}-2 x \,x^{-80 x^{2}} \left ({\mathrm e}^{x}\right )^{80 x^{2}} x^{5 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right ) x^{3}} \left ({\mathrm e}^{x}\right )^{-5 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right ) x^{3}} \left ({\mathrm e}^{x}\right )^{10 x^{3} \ln \relax (x )} x^{-5 i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}} x^{-5 i \pi \,\mathrm {csgn}\left (i x \right ) x^{3}} \left ({\mathrm e}^{x}\right )^{5 i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}} \left ({\mathrm e}^{x}\right )^{5 i \pi \,\mathrm {csgn}\left (i x \right ) x^{3}} x^{5 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) x^{3}} \left ({\mathrm e}^{x}\right )^{-5 i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) x^{3}} {\mathrm e}^{-\frac {x \left (-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )^{2}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{5} \mathrm {csgn}\left (i x \right )-20 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right )+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{6}+10 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{5} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-5 x^{2} \pi ^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{4} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )^{2}-160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3}-160 i x \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right )+160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )+160 i x \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )+20 x^{2} \ln \relax (x )^{2}+20 x^{2} \ln \left ({\mathrm e}^{x}\right )^{2}+1204\right )}{4}}+x^{2}\)	\(1157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-30*x^2*ln(x/exp(x))^2+(20*x^3-20*x^2-320*x)*ln(x/exp(x))+160*x^2-160*x-602)*exp(-5*x^3*ln(x/exp(x))^2-80
*x^2*ln(x/exp(x))-301*x)^2+(30*x^3*ln(x/exp(x))^2+(-20*x^4+20*x^3+320*x^2)*ln(x/exp(x))-160*x^3+160*x^2+602*x-
2)*exp(-5*x^3*ln(x/exp(x))^2-80*x^2*ln(x/exp(x))-301*x)+2*x,x,method=_RETURNVERBOSE)

[Out]

(exp(x)^(-5*I*Pi*csgn(I*x*exp(-x))*x^3))^2*(x^(5*I*Pi*csgn(I*x*exp(-x))*x^3))^2*(exp(x)^(5*I*Pi*csgn(I*x)*x^3)
)^2*(exp(x)^(5*I*Pi*csgn(I*exp(-x))*x^3))^2*(x^(-5*I*Pi*csgn(I*x)*x^3))^2*(x^(-5*I*Pi*csgn(I*exp(-x))*x^3))^2*
(exp(x)^(10*x^3*ln(x)))^2*(exp(x)^(-5*I*Pi*csgn(I*x*exp(-x))*csgn(I*exp(-x))*csgn(I*x)*x^3))^2*(x^(5*I*Pi*csgn
(I*x*exp(-x))*csgn(I*exp(-x))*csgn(I*x)*x^3))^2*(exp(x)^(80*x^2))^2*(x^(-80*x^2))^2*exp(-1/2*x*(-5*x^2*Pi^2*cs
gn(I*x*exp(-x))^4*csgn(I*x)^2+10*x^2*Pi^2*csgn(I*x*exp(-x))^3*csgn(I*x)^2*csgn(I*exp(-x))-5*x^2*Pi^2*csgn(I*x*
exp(-x))^2*csgn(I*exp(-x))^2*csgn(I*x)^2+10*x^2*Pi^2*csgn(I*x*exp(-x))^5*csgn(I*x)-20*x^2*Pi^2*csgn(I*x*exp(-x
))^4*csgn(I*exp(-x))*csgn(I*x)+10*x^2*Pi^2*csgn(I*x*exp(-x))^3*csgn(I*exp(-x))^2*csgn(I*x)-5*x^2*Pi^2*csgn(I*x
*exp(-x))^6+10*x^2*Pi^2*csgn(I*x*exp(-x))^5*csgn(I*exp(-x))-5*x^2*Pi^2*csgn(I*x*exp(-x))^4*csgn(I*exp(-x))^2-1
60*I*x*Pi*csgn(I*x*exp(-x))^3-160*I*x*Pi*csgn(I*x*exp(-x))*csgn(I*exp(-x))*csgn(I*x)+160*I*x*Pi*csgn(I*x*exp(-
x))^2*csgn(I*x)+160*I*x*Pi*csgn(I*x*exp(-x))^2*csgn(I*exp(-x))+20*x^2*ln(x)^2+20*x^2*ln(exp(x))^2+1204))-2*x*x
^(-80*x^2)*exp(x)^(80*x^2)*x^(5*I*Pi*csgn(I*x*exp(-x))*csgn(I*exp(-x))*csgn(I*x)*x^3)*exp(x)^(-5*I*Pi*csgn(I*x
*exp(-x))*csgn(I*exp(-x))*csgn(I*x)*x^3)*exp(x)^(10*x^3*ln(x))*x^(-5*I*Pi*csgn(I*exp(-x))*x^3)*x^(-5*I*Pi*csgn
(I*x)*x^3)*exp(x)^(5*I*Pi*csgn(I*exp(-x))*x^3)*exp(x)^(5*I*Pi*csgn(I*x)*x^3)*x^(5*I*Pi*csgn(I*x*exp(-x))*x^3)*
exp(x)^(-5*I*Pi*csgn(I*x*exp(-x))*x^3)*exp(-1/4*x*(-5*x^2*Pi^2*csgn(I*x*exp(-x))^4*csgn(I*x)^2+10*x^2*Pi^2*csg
n(I*x*exp(-x))^3*csgn(I*x)^2*csgn(I*exp(-x))-5*x^2*Pi^2*csgn(I*x*exp(-x))^2*csgn(I*exp(-x))^2*csgn(I*x)^2+10*x
^2*Pi^2*csgn(I*x*exp(-x))^5*csgn(I*x)-20*x^2*Pi^2*csgn(I*x*exp(-x))^4*csgn(I*exp(-x))*csgn(I*x)+10*x^2*Pi^2*cs
gn(I*x*exp(-x))^3*csgn(I*exp(-x))^2*csgn(I*x)-5*x^2*Pi^2*csgn(I*x*exp(-x))^6+10*x^2*Pi^2*csgn(I*x*exp(-x))^5*c
sgn(I*exp(-x))-5*x^2*Pi^2*csgn(I*x*exp(-x))^4*csgn(I*exp(-x))^2-160*I*x*Pi*csgn(I*x*exp(-x))^3-160*I*x*Pi*csgn
(I*x*exp(-x))*csgn(I*exp(-x))*csgn(I*x)+160*I*x*Pi*csgn(I*x*exp(-x))^2*csgn(I*x)+160*I*x*Pi*csgn(I*x*exp(-x))^
2*csgn(I*exp(-x))+20*x^2*ln(x)^2+20*x^2*ln(exp(x))^2+1204))+x^2

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maxima [B]  time = 0.67, size = 83, normalized size = 2.52 \begin {gather*} x^{2} - 2 \, x e^{\left (-5 \, x^{5} + 10 \, x^{4} \log \relax (x) - 5 \, x^{3} \log \relax (x)^{2} + 80 \, x^{3} - 80 \, x^{2} \log \relax (x) - 301 \, x\right )} + e^{\left (-10 \, x^{5} + 20 \, x^{4} \log \relax (x) - 10 \, x^{3} \log \relax (x)^{2} + 160 \, x^{3} - 160 \, x^{2} \log \relax (x) - 602 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-30*x^2*log(x/exp(x))^2+(20*x^3-20*x^2-320*x)*log(x/exp(x))+160*x^2-160*x-602)*exp(-5*x^3*log(x/exp
(x))^2-80*x^2*log(x/exp(x))-301*x)^2+(30*x^3*log(x/exp(x))^2+(-20*x^4+20*x^3+320*x^2)*log(x/exp(x))-160*x^3+16
0*x^2+602*x-2)*exp(-5*x^3*log(x/exp(x))^2-80*x^2*log(x/exp(x))-301*x)+2*x,x, algorithm="maxima")

[Out]

x^2 - 2*x*e^(-5*x^5 + 10*x^4*log(x) - 5*x^3*log(x)^2 + 80*x^3 - 80*x^2*log(x) - 301*x) + e^(-10*x^5 + 20*x^4*l
og(x) - 10*x^3*log(x)^2 + 160*x^3 - 160*x^2*log(x) - 602*x)

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mupad [B]  time = 1.46, size = 92, normalized size = 2.79 \begin {gather*} x^2+\frac {x^{20\,x^4}\,{\mathrm {e}}^{-602\,x}\,{\mathrm {e}}^{-10\,x^5}\,{\mathrm {e}}^{160\,x^3}\,{\mathrm {e}}^{-10\,x^3\,{\ln \relax (x)}^2}}{x^{160\,x^2}}-\frac {2\,x\,x^{10\,x^4}\,{\mathrm {e}}^{-301\,x}\,{\mathrm {e}}^{-5\,x^5}\,{\mathrm {e}}^{80\,x^3}\,{\mathrm {e}}^{-5\,x^3\,{\ln \relax (x)}^2}}{x^{80\,x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(- 301*x - 5*x^3*log(x*exp(-x))^2 - 80*x^2*log(x*exp(-x)))*(602*x + 30*x^3*log(x*exp(-x))^2 + 160
*x^2 - 160*x^3 + log(x*exp(-x))*(320*x^2 + 20*x^3 - 20*x^4) - 2) - exp(- 602*x - 10*x^3*log(x*exp(-x))^2 - 160
*x^2*log(x*exp(-x)))*(160*x + 30*x^2*log(x*exp(-x))^2 + log(x*exp(-x))*(320*x + 20*x^2 - 20*x^3) - 160*x^2 + 6
02),x)

[Out]

x^2 + (x^(20*x^4)*exp(-602*x)*exp(-10*x^5)*exp(160*x^3)*exp(-10*x^3*log(x)^2))/x^(160*x^2) - (2*x*x^(10*x^4)*e
xp(-301*x)*exp(-5*x^5)*exp(80*x^3)*exp(-5*x^3*log(x)^2))/x^(80*x^2)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-30*x**2*ln(x/exp(x))**2+(20*x**3-20*x**2-320*x)*ln(x/exp(x))+160*x**2-160*x-602)*exp(-5*x**3*ln(x/
exp(x))**2-80*x**2*ln(x/exp(x))-301*x)**2+(30*x**3*ln(x/exp(x))**2+(-20*x**4+20*x**3+320*x**2)*ln(x/exp(x))-16
0*x**3+160*x**2+602*x-2)*exp(-5*x**3*ln(x/exp(x))**2-80*x**2*ln(x/exp(x))-301*x)+2*x,x)

[Out]

Timed out

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