3.88.44 \(\int (3+2 \log (x)) \, dx\) [8744]

Optimal. Leaf size=13 \[ 5+e^3+x+\log (4)+2 x \log (x) \]

[Out]

5+x+exp(3)+2*ln(2)+2*x*ln(x)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 2, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2332} \begin {gather*} x+2 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + 2*Log[x],x]

[Out]

x + 2*x*Log[x]

Rule 2332

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

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.54 \begin {gather*} x+2 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + 2*Log[x],x]

[Out]

x + 2*x*Log[x]

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Maple [A]
time = 0.12, size = 8, normalized size = 0.62

method	result	size
default	\(x +2 x \ln \left (x \right )\)	\(8\)
norman	\(x +2 x \ln \left (x \right )\)	\(8\)
risch	\(x +2 x \ln \left (x \right )\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*ln(x)+3,x,method=_RETURNVERBOSE)

[Out]

x+2*x*ln(x)

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Maxima [A]
time = 0.25, size = 7, normalized size = 0.54 \begin {gather*} 2 \, x \log \left (x\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+3,x, algorithm="maxima")

[Out]

2*x*log(x) + x

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Fricas [A]
time = 0.35, size = 7, normalized size = 0.54 \begin {gather*} 2 \, x \log \left (x\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+3,x, algorithm="fricas")

[Out]

2*x*log(x) + x

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Sympy [A]
time = 0.02, size = 7, normalized size = 0.54 \begin {gather*} 2 x \log {\left (x \right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*ln(x)+3,x)

[Out]

2*x*log(x) + x

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Giac [A]
time = 0.42, size = 7, normalized size = 0.54 \begin {gather*} 2 \, x \log \left (x\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+3,x, algorithm="giac")

[Out]

2*x*log(x) + x

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Mupad [B]
time = 5.33, size = 8, normalized size = 0.62 \begin {gather*} x\,\left (2\,\ln \left (x\right )+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*log(x) + 3,x)

[Out]

x*(2*log(x) + 1)

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