3.94.18 \(\int (-2-2 e^x-2 \log (x)) \, dx\)

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

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2194, 2295} \begin {gather*} -2 e^x-2 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2 - 2*E^x - 2*Log[x],x]

[Out]

-2*E^x - 2*x*Log[x]

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 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} &=-2 x-2 \int e^x \, dx-2 \int \log (x) \, dx\\ &=-2 e^x-2 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.62 \begin {gather*} -2 \left (e^x+x \log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2 - 2*E^x - 2*Log[x],x]

[Out]

-2*(E^x + x*Log[x])

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fricas [A]  time = 1.01, size = 10, normalized size = 0.62 \begin {gather*} -2 \, x \log \relax (x) - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(x)-2*exp(x)-2,x, algorithm="fricas")

[Out]

-2*x*log(x) - 2*e^x

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giac [A]  time = 0.18, size = 10, normalized size = 0.62 \begin {gather*} -2 \, x \log \relax (x) - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(x)-2*exp(x)-2,x, algorithm="giac")

[Out]

-2*x*log(x) - 2*e^x

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maple [A]  time = 0.02, size = 11, normalized size = 0.69

method	result	size
default	\(-2 \,{\mathrm e}^{x}-2 x \ln \relax (x )\)	\(11\)
norman	\(-2 \,{\mathrm e}^{x}-2 x \ln \relax (x )\)	\(11\)
risch	\(-2 \,{\mathrm e}^{x}-2 x \ln \relax (x )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*ln(x)-2*exp(x)-2,x,method=_RETURNVERBOSE)

[Out]

-2*exp(x)-2*x*ln(x)

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maxima [A]  time = 0.38, size = 10, normalized size = 0.62 \begin {gather*} -2 \, x \log \relax (x) - 2 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*log(x)-2*exp(x)-2,x, algorithm="maxima")

[Out]

-2*x*log(x) - 2*e^x

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mupad [B]  time = 7.02, size = 10, normalized size = 0.62 \begin {gather*} -2\,{\mathrm {e}}^x-2\,x\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*exp(x) - 2*log(x) - 2,x)

[Out]

- 2*exp(x) - 2*x*log(x)

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sympy [A]  time = 0.23, size = 12, normalized size = 0.75 \begin {gather*} - 2 x \log {\relax (x )} - 2 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*ln(x)-2*exp(x)-2,x)

[Out]

-2*x*log(x) - 2*exp(x)

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