3.61.70 \(\int (-3-4 x+e^{e^x} (-1-e^x x)+\log (x^3)) \, dx\)

Optimal. Leaf size=18 \[ x \left (-6-e^{e^x}-2 x+\log \left (x^3\right )\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.28, number of steps used = 3, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {2288, 2295} \begin {gather*} x \log \left (x^3\right )-2 x^2-e^{e^x} x-6 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 - 4*x + E^E^x*(-1 - E^x*x) + Log[x^3],x]

[Out]

-6*x - E^E^x*x - 2*x^2 + x*Log[x^3]

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 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-3 x-2 x^2+\int e^{e^x} \left (-1-e^x x\right ) \, dx+\int \log \left (x^3\right ) \, dx\\ &=-6 x-e^{e^x} x-2 x^2+x \log \left (x^3\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 23, normalized size = 1.28 \begin {gather*} -6 x-e^{e^x} x-2 x^2+x \log \left (x^3\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 - 4*x + E^E^x*(-1 - E^x*x) + Log[x^3],x]

[Out]

-6*x - E^E^x*x - 2*x^2 + x*Log[x^3]

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fricas [A]  time = 0.68, size = 21, normalized size = 1.17 \begin {gather*} -2 \, x^{2} - x e^{\left (e^{x}\right )} + x \log \left (x^{3}\right ) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x-1)*exp(exp(x))+log(x^3)-4*x-3,x, algorithm="fricas")

[Out]

-2*x^2 - x*e^(e^x) + x*log(x^3) - 6*x

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giac [A]  time = 0.21, size = 21, normalized size = 1.17 \begin {gather*} -2 \, x^{2} - x e^{\left (e^{x}\right )} + x \log \left (x^{3}\right ) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x-1)*exp(exp(x))+log(x^3)-4*x-3,x, algorithm="giac")

[Out]

-2*x^2 - x*e^(e^x) + x*log(x^3) - 6*x

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maple [A]  time = 0.05, size = 22, normalized size = 1.22

method	result	size
default	\(-6 x -x \,{\mathrm e}^{{\mathrm e}^{x}}-2 x^{2}+x \ln \left (x^{3}\right )\)	\(22\)
norman	\(-6 x -x \,{\mathrm e}^{{\mathrm e}^{x}}-2 x^{2}+x \ln \left (x^{3}\right )\)	\(22\)
risch	\(-6 x -x \,{\mathrm e}^{{\mathrm e}^{x}}-2 x^{2}+x \ln \left (x^{3}\right )\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(x)*x-1)*exp(exp(x))+ln(x^3)-4*x-3,x,method=_RETURNVERBOSE)

[Out]

-6*x-x*exp(exp(x))-2*x^2+x*ln(x^3)

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maxima [A]  time = 0.35, size = 21, normalized size = 1.17 \begin {gather*} -2 \, x^{2} - x e^{\left (e^{x}\right )} + x \log \left (x^{3}\right ) - 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x-1)*exp(exp(x))+log(x^3)-4*x-3,x, algorithm="maxima")

[Out]

-2*x^2 - x*e^(e^x) + x*log(x^3) - 6*x

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mupad [B]  time = 4.29, size = 17, normalized size = 0.94 \begin {gather*} -x\,\left (2\,x+{\mathrm {e}}^{{\mathrm {e}}^x}-\ln \left (x^3\right )+6\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x^3) - 4*x - exp(exp(x))*(x*exp(x) + 1) - 3,x)

[Out]

-x*(2*x + exp(exp(x)) - log(x^3) + 6)

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sympy [A]  time = 0.29, size = 20, normalized size = 1.11 \begin {gather*} - 2 x^{2} - x e^{e^{x}} + x \log {\left (x^{3} \right )} - 6 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(x)*x-1)*exp(exp(x))+ln(x**3)-4*x-3,x)

[Out]

-2*x**2 - x*exp(exp(x)) + x*log(x**3) - 6*x

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