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

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

[Out]

-x + x*Log[x]

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Rubi [A]  time = 0.0009977, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, 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*}

Mathematica [A]  time = 0.0005906, size = 8, normalized size = 1. \[ x \log (x)-x \]

Antiderivative was successfully verified.

[In]

Integrate[Log[x],x]

[Out]

-x + x*Log[x]

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Maple [A]  time = 0.001, size = 9, normalized size = 1.1 \begin{align*} -x+x\ln \left ( x \right ) \end{align*}

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 = 0.921812, size = 11, normalized size = 1.38 \begin{align*} x \log \left (x\right ) - x \end{align*}

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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Fricas [A]  time = 1.82787, size = 19, normalized size = 2.38 \begin{align*} x \log \left (x\right ) - x \end{align*}

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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Sympy [A]  time = 0.076374, size = 5, normalized size = 0.62 \begin{align*} x \log{\left (x \right )} - x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(x),x)

[Out]

x*log(x) - x

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Giac [A]  time = 1.05865, size = 11, normalized size = 1.38 \begin{align*} x \log \left (x\right ) - x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(x),x, algorithm="giac")

[Out]

x*log(x) - x