3.96.19 \(\int (1-4 e^3-e^3 \log (x)) \, dx\)

Optimal. Leaf size=15 \[ -9+x \left (1-e^3 (3+\log (x))\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.53, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2295} \begin {gather*} \left (1-4 e^3\right ) x+e^3 x-e^3 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 4*E^3 - E^3*Log[x],x]

[Out]

E^3*x + (1 - 4*E^3)*x - E^3*x*Log[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} &=\left (1-4 e^3\right ) x-e^3 \int \log (x) \, dx\\ &=e^3 x+\left (1-4 e^3\right ) x-e^3 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} x-3 e^3 x-e^3 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - 4*E^3 - E^3*Log[x],x]

[Out]

x - 3*E^3*x - E^3*x*Log[x]

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fricas [A]  time = 0.55, size = 14, normalized size = 0.93 \begin {gather*} -x e^{3} \log \relax (x) - 3 \, x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*e^3*log(x) - 3*x*e^3 + x

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giac [A]  time = 0.94, size = 19, normalized size = 1.27 \begin {gather*} -{\left (x \log \relax (x) - x\right )} e^{3} - 4 \, x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x*log(x) - x)*e^3 - 4*x*e^3 + x

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maple [A]  time = 0.02, size = 15, normalized size = 1.00

method	result	size
default	\(x -x \,{\mathrm e}^{3} \ln \relax (x )-3 x \,{\mathrm e}^{3}\)	\(15\)
risch	\(x -x \,{\mathrm e}^{3} \ln \relax (x )-3 x \,{\mathrm e}^{3}\)	\(15\)
norman	\(\left (1-3 \,{\mathrm e}^{3}\right ) x -x \,{\mathrm e}^{3} \ln \relax (x )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x-x*exp(3)*ln(x)-3*x*exp(3)

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maxima [A]  time = 0.34, size = 19, normalized size = 1.27 \begin {gather*} -{\left (x \log \relax (x) - x\right )} e^{3} - 4 \, x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x*log(x) - x)*e^3 - 4*x*e^3 + x

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mupad [B]  time = 7.54, size = 14, normalized size = 0.93 \begin {gather*} -x\,\left (3\,{\mathrm {e}}^3+{\mathrm {e}}^3\,\ln \relax (x)-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - exp(3)*log(x) - 4*exp(3),x)

[Out]

-x*(3*exp(3) + exp(3)*log(x) - 1)

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sympy [A]  time = 0.09, size = 15, normalized size = 1.00 \begin {gather*} - x e^{3} \log {\relax (x )} + x \left (1 - 3 e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*exp(3)*log(x) + x*(1 - 3*exp(3))

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