3.63.84 \(\int \frac {e^{\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e (16 x+8 x \log (2)+x \log ^2(2))}} (-9-48 x-24 x \log (2)-3 x \log ^2(2)+e^e (16 x+8 x \log (2)+x \log ^2(2)))}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e (16 x+8 x \log (2)+x \log ^2(2))} \, dx\)

Optimal. Leaf size=24 \[ e^{\frac {9 x}{\left (-3+e^e\right ) (4 x+x \log (2))^2}} x \]

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Rubi [A]  time = 0.41, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6, 2288} \begin {gather*} x e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(9/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x*Log[2]^2)))*(-9 - 48*x - 24*x*Log[2
] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x*Log[2]^2)))/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*
x*Log[2] + x*Log[2]^2)),x]

[Out]

x/E^(9/((3 - E^E)*x*(4 + Log[2])^2))

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

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]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}\right ) \left (-9+x (-48-24 \log (2))-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx\\ &=\int \frac {\exp \left (\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}\right ) \left (-9+x \left (-48-24 \log (2)-3 \log ^2(2)\right )+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx\\ &=\int \frac {\exp \left (\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}\right ) \left (-9+x \left (-48-24 \log (2)-3 \log ^2(2)\right )+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{x (-48-24 \log (2))-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx\\ &=\int \frac {\exp \left (\frac {9}{-48 x-24 x \log (2)-3 x \log ^2(2)+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )}\right ) \left (-9+x \left (-48-24 \log (2)-3 \log ^2(2)\right )+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )\right )}{x \left (-48-24 \log (2)-3 \log ^2(2)\right )+e^e \left (16 x+8 x \log (2)+x \log ^2(2)\right )} \, dx\\ &=e^{-\frac {9}{\left (3-e^e\right ) x (4+\log (2))^2}} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 22, normalized size = 0.92 \begin {gather*} e^{\frac {9}{\left (-3+e^e\right ) x (4+\log (2))^2}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(9/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x*Log[2]^2)))*(-9 - 48*x - 24*x
*Log[2] - 3*x*Log[2]^2 + E^E*(16*x + 8*x*Log[2] + x*Log[2]^2)))/(-48*x - 24*x*Log[2] - 3*x*Log[2]^2 + E^E*(16*
x + 8*x*Log[2] + x*Log[2]^2)),x]

[Out]

E^(9/((-3 + E^E)*x*(4 + Log[2])^2))*x

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fricas [A]  time = 0.82, size = 43, normalized size = 1.79 \begin {gather*} x e^{\left (-\frac {9}{3 \, x \log \relax (2)^{2} - {\left (x \log \relax (2)^{2} + 8 \, x \log \relax (2) + 16 \, x\right )} e^{e} + 24 \, x \log \relax (2) + 48 \, x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x-9)*exp(9/((x*log(2)^2+8*x*lo
g(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-
24*x*log(2)-48*x),x, algorithm="fricas")

[Out]

x*e^(-9/(3*x*log(2)^2 - (x*log(2)^2 + 8*x*log(2) + 16*x)*e^e + 24*x*log(2) + 48*x))

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giac [B]  time = 0.51, size = 806, normalized size = 33.58 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x-9)*exp(9/((x*log(2)^2+8*x*lo
g(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-
24*x*log(2)-48*x),x, algorithm="giac")

[Out]

(e^e*log(2)^2 + 8*e^e*log(2) - 3*log(2)^2 + 16*e^e - 24*log(2) - 48)*e^(9/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3
*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x))/(e^(2*e)*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^
2 + 16*x*e^e - 24*x*log(2) - 48*x) - 6*e^e*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e
- 24*x*log(2) - 48*x) + 16*e^(2*e)*log(2)^3/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x
*log(2) - 48*x) - 96*e^e*log(2)^3/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 4
8*x) + 9*log(2)^4/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 96*e^(2*e
)*log(2)^2/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) - 576*e^e*log(2)^2
/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 144*log(2)^3/(x*e^e*log(2)
^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 256*e^(2*e)*log(2)/(x*e^e*log(2)^2 + 8*x
*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) - 1536*e^e*log(2)/(x*e^e*log(2)^2 + 8*x*e^e*log(2)
- 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 864*log(2)^2/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^
2 + 16*x*e^e - 24*x*log(2) - 48*x) + 256*e^(2*e)/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e -
24*x*log(2) - 48*x) - 1536*e^e/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x
) + 2304*log(2)/(x*e^e*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x) + 2304/(x*e^e
*log(2)^2 + 8*x*e^e*log(2) - 3*x*log(2)^2 + 16*x*e^e - 24*x*log(2) - 48*x))

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maple [A]  time = 0.54, size = 22, normalized size = 0.92

method	result	size
risch	\(x \,{\mathrm e}^{\frac {9}{x \left (4+\ln \relax (2)\right )^{2} \left ({\mathrm e}^{{\mathrm e}}-3\right )}}\)	\(22\)
gosper	\(x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}}\)	\(43\)
norman	\(x \,{\mathrm e}^{\frac {9}{\left (x \ln \relax (2)^{2}+8 x \ln \relax (2)+16 x \right ) {\mathrm e}^{{\mathrm e}}-3 x \ln \relax (2)^{2}-24 x \ln \relax (2)-48 x}}\)	\(43\)
derivativedivides	\(-\frac {9 \left (\expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )+\frac {16 x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}}}{3}+\frac {48 \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}+\frac {8 \ln \relax (2) {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{3}+\frac {24 \ln \relax (2) \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}+\frac {\ln \relax (2)^{2} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{3}+\frac {3 \ln \relax (2)^{2} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {16 \,{\mathrm e}^{{\mathrm e}} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {16 \,{\mathrm e}^{{\mathrm e}} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2) {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2) \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}\)	\(841\)
default	\(-\frac {9 \left (\expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )+\frac {16 x \,{\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}}}{3}+\frac {48 \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}+\frac {8 \ln \relax (2) {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{3}+\frac {24 \ln \relax (2) \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}+\frac {\ln \relax (2)^{2} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{3}+\frac {3 \ln \relax (2)^{2} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {16 \,{\mathrm e}^{{\mathrm e}} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {16 \,{\mathrm e}^{{\mathrm e}} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2) {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2) \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}-\frac {{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2} {\mathrm e}^{\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}} x}{9}-\frac {{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2} \expIntegralEi \left (1, -\frac {9}{x \left ({\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48\right )}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}\right )}{{\mathrm e}^{{\mathrm e}} \ln \relax (2)^{2}+8 \,{\mathrm e}^{{\mathrm e}} \ln \relax (2)-3 \ln \relax (2)^{2}+16 \,{\mathrm e}^{{\mathrm e}}-24 \ln \relax (2)-48}\)	\(841\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x*ln(2)^2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x-9)*exp(9/((x*ln(2)^2+8*x*ln(2)+16*x)*e
xp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x))/((x*ln(2)^2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)^2-24*x*ln(2)-48*x),
x,method=_RETURNVERBOSE)

[Out]

x*exp(9/x/(4+ln(2))^2/(exp(exp(1))-3))

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maxima [C]  time = 0.67, size = 266, normalized size = 11.08 \begin {gather*} \frac {9 \, {\rm Ei}\left (\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}} - \frac {9 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right ) \log \relax (2)^{2}}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} - \frac {72 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right ) \log \relax (2)}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} + \frac {27 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right ) \log \relax (2)^{2}}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} - \frac {144 \, e^{e} \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} + \frac {216 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right ) \log \relax (2)}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} + \frac {432 \, \Gamma \left (-1, -\frac {9}{x {\left (e^{e} - 3\right )} {\left (\log \relax (2) + 4\right )}^{2}}\right )}{{\left (e^{e} - 3\right )}^{2} {\left (\log \relax (2) + 4\right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x-9)*exp(9/((x*log(2)^2+8*x*lo
g(2)+16*x)*exp(exp(1))-3*x*log(2)^2-24*x*log(2)-48*x))/((x*log(2)^2+8*x*log(2)+16*x)*exp(exp(1))-3*x*log(2)^2-
24*x*log(2)-48*x),x, algorithm="maxima")

[Out]

9*Ei(9/(x*(e^e - 3)*(log(2) + 4)^2))/((e^e - 3)*(log(2) + 4)^2) - 9*e^e*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)
^2))*log(2)^2/((e^e - 3)^2*(log(2) + 4)^4) - 72*e^e*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))*log(2)/((e^e -
3)^2*(log(2) + 4)^4) + 27*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))*log(2)^2/((e^e - 3)^2*(log(2) + 4)^4) - 1
44*e^e*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))/((e^e - 3)^2*(log(2) + 4)^4) + 216*gamma(-1, -9/(x*(e^e - 3)
*(log(2) + 4)^2))*log(2)/((e^e - 3)^2*(log(2) + 4)^4) + 432*gamma(-1, -9/(x*(e^e - 3)*(log(2) + 4)^2))/((e^e -
3)^2*(log(2) + 4)^4)

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mupad [B]  time = 4.31, size = 47, normalized size = 1.96 \begin {gather*} x\,{\mathrm {e}}^{-\frac {9}{48\,x+24\,x\,\ln \relax (2)-16\,x\,{\mathrm {e}}^{\mathrm {e}}+3\,x\,{\ln \relax (2)}^2-8\,x\,{\mathrm {e}}^{\mathrm {e}}\,\ln \relax (2)-x\,{\mathrm {e}}^{\mathrm {e}}\,{\ln \relax (2)}^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-9/(48*x + 24*x*log(2) - exp(exp(1))*(16*x + 8*x*log(2) + x*log(2)^2) + 3*x*log(2)^2))*(48*x + 24*x*l
og(2) - exp(exp(1))*(16*x + 8*x*log(2) + x*log(2)^2) + 3*x*log(2)^2 + 9))/(48*x + 24*x*log(2) - exp(exp(1))*(1
6*x + 8*x*log(2) + x*log(2)^2) + 3*x*log(2)^2),x)

[Out]

x*exp(-9/(48*x + 24*x*log(2) - 16*x*exp(exp(1)) + 3*x*log(2)^2 - 8*x*exp(exp(1))*log(2) - x*exp(exp(1))*log(2)
^2))

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sympy [A]  time = 0.28, size = 44, normalized size = 1.83 \begin {gather*} x e^{\frac {9}{- 48 x - 24 x \log {\relax (2 )} - 3 x \log {\relax (2 )}^{2} + \left (x \log {\relax (2 )}^{2} + 8 x \log {\relax (2 )} + 16 x\right ) e^{e}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x*ln(2)**2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x*ln(2)-48*x-9)*exp(9/((x*ln(2)**2+8*x*ln(2
)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x*ln(2)-48*x))/((x*ln(2)**2+8*x*ln(2)+16*x)*exp(exp(1))-3*x*ln(2)**2-24*x*
ln(2)-48*x),x)

[Out]

x*exp(9/(-48*x - 24*x*log(2) - 3*x*log(2)**2 + (x*log(2)**2 + 8*x*log(2) + 16*x)*exp(E)))

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