3.53 \(\int \log (x) \, dx\)

Optimal. Leaf size=8 \[ x \log (x)-x \]

[Out]

-x+x*ln(x)

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2295} \[ x \log (x)-x \]

Antiderivative was successfully verified.

[In]

Int[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 {align*} \int \log (x) \, dx &=-x+x \log (x)\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \[ x \log (x)-x \]

Antiderivative was successfully verified.

[In]

Integrate[Log[x],x]

[Out]

-x + x*Log[x]

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fricas [A]  time = 0.44, size = 8, normalized size = 1.00 \[ x \log \relax (x) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(x) - x

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giac [A]  time = 1.07, size = 8, normalized size = 1.00 \[ x \log \relax (x) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x),x, algorithm="giac")

[Out]

x*log(x) - x

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maple [A]  time = 0.00, size = 9, normalized size = 1.12 \[ x \ln \relax (x )-x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(x),x)

[Out]

-x+x*ln(x)

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maxima [A]  time = 0.41, size = 8, normalized size = 1.00 \[ x \log \relax (x) - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(x) - x

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mupad [B]  time = 0.02, size = 6, normalized size = 0.75 \[ x\,\left (\ln \relax (x)-1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x),x)

[Out]

x*(log(x) - 1)

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sympy [A]  time = 0.08, size = 5, normalized size = 0.62 \[ x \log {\relax (x )} - x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x),x)

[Out]

x*log(x) - x

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