3.13.45 \(\int (2+\log (x)) \, dx\)

Optimal. Leaf size=13 \[ 3+x-\log ^2(2)+x \log (x) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.46, number of steps used = 2, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2295} \begin {gather*} x+x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2 + Log[x],x]

[Out]

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

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.46 \begin {gather*} x+x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2 + Log[x],x]

[Out]

x + x*Log[x]

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fricas [A]  time = 0.53, size = 6, normalized size = 0.46 \begin {gather*} x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+2,x, algorithm="fricas")

[Out]

x*log(x) + x

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giac [A]  time = 0.53, size = 6, normalized size = 0.46 \begin {gather*} x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+2,x, algorithm="giac")

[Out]

x*log(x) + x

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maple [A]  time = 0.01, size = 7, normalized size = 0.54

method	result	size
default	\(x \ln \relax (x )+x\)	\(7\)
norman	\(x \ln \relax (x )+x\)	\(7\)
risch	\(x \ln \relax (x )+x\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(x)+2,x,method=_RETURNVERBOSE)

[Out]

x*ln(x)+x

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maxima [A]  time = 0.46, size = 6, normalized size = 0.46 \begin {gather*} x \log \relax (x) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x)+2,x, algorithm="maxima")

[Out]

x*log(x) + x

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mupad [B]  time = 0.85, size = 6, normalized size = 0.46 \begin {gather*} x\,\left (\ln \relax (x)+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x) + 2,x)

[Out]

x*(log(x) + 1)

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sympy [A]  time = 0.07, size = 5, normalized size = 0.38 \begin {gather*} x \log {\relax (x )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x)+2,x)

[Out]

x*log(x) + x

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