3.84.49 \(\int (-3-e-2 x-3 \log (x)) \, dx\)

Optimal. Leaf size=13 \[ x (-e-x-3 \log (x)) \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.54, number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2295} \begin {gather*} -x^2-(3+e) x+3 x-3 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 - E - 2*x - 3*Log[x],x]

[Out]

3*x - (3 + E)*x - x^2 - 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} &=-((3+e) x)-x^2-3 \int \log (x) \, dx\\ &=3 x-(3+e) x-x^2-3 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.15 \begin {gather*} -e x-x^2-3 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 - E - 2*x - 3*Log[x],x]

[Out]

-(E*x) - x^2 - 3*x*Log[x]

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fricas [A]  time = 0.58, size = 16, normalized size = 1.23 \begin {gather*} -x^{2} - x e - 3 \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(x)-exp(1)-2*x-3,x, algorithm="fricas")

[Out]

-x^2 - x*e - 3*x*log(x)

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giac [A]  time = 2.07, size = 16, normalized size = 1.23 \begin {gather*} -x^{2} - x e - 3 \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(x)-exp(1)-2*x-3,x, algorithm="giac")

[Out]

-x^2 - x*e - 3*x*log(x)

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maple [A]  time = 0.03, size = 17, normalized size = 1.31

method	result	size
default	\(-x^{2}-x \,{\mathrm e}-3 x \ln \relax (x )\)	\(17\)
norman	\(-x^{2}-x \,{\mathrm e}-3 x \ln \relax (x )\)	\(17\)
risch	\(-x^{2}-x \,{\mathrm e}-3 x \ln \relax (x )\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*ln(x)-exp(1)-2*x-3,x,method=_RETURNVERBOSE)

[Out]

-x^2-x*exp(1)-3*x*ln(x)

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maxima [A]  time = 0.36, size = 16, normalized size = 1.23 \begin {gather*} -x^{2} - x e - 3 \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*log(x)-exp(1)-2*x-3,x, algorithm="maxima")

[Out]

-x^2 - x*e - 3*x*log(x)

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mupad [B]  time = 5.46, size = 11, normalized size = 0.85 \begin {gather*} -x\,\left (x+\mathrm {e}+3\,\ln \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*x - exp(1) - 3*log(x) - 3,x)

[Out]

-x*(x + exp(1) + 3*log(x))

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sympy [A]  time = 0.08, size = 15, normalized size = 1.15 \begin {gather*} - x^{2} - 3 x \log {\relax (x )} - e x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*ln(x)-exp(1)-2*x-3,x)

[Out]

-x**2 - 3*x*log(x) - E*x

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