3.70.88 \(\int (-1+\log (2)) \, dx\)

Optimal. Leaf size=23 \[ 6-e^3-x+x^3+x \left (-x^2+\log (2)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \begin {gather*} -x (1-\log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + Log[2],x]

[Out]

-(x*(1 - Log[2]))

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x (1-\log (2))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.35 \begin {gather*} -x+x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + Log[2],x]

[Out]

-x + x*Log[2]

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fricas [A]  time = 0.67, size = 8, normalized size = 0.35 \begin {gather*} x \log \relax (2) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2) - x

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giac [A]  time = 0.19, size = 6, normalized size = 0.26 \begin {gather*} x {\left (\log \relax (2) - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(log(2) - 1)

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maple [A]  time = 0.01, size = 7, normalized size = 0.30

method	result	size
default	\(x \left (\ln \relax (2)-1\right )\)	\(7\)
norman	\(x \left (\ln \relax (2)-1\right )\)	\(7\)
risch	\(x \ln \relax (2)-x\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(ln(2)-1)

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maxima [A]  time = 0.37, size = 6, normalized size = 0.26 \begin {gather*} x {\left (\log \relax (2) - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(log(2) - 1)

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mupad [B]  time = 0.00, size = 6, normalized size = 0.26 \begin {gather*} x\,\left (\ln \relax (2)-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(2) - 1,x)

[Out]

x*(log(2) - 1)

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sympy [A]  time = 0.04, size = 5, normalized size = 0.22 \begin {gather*} x \left (-1 + \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(2)-1,x)

[Out]

x*(-1 + log(2))

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