\(\int (-1+\log (2)) \, dx\) [6988]

Optimal result

Integrand size = 4, antiderivative size = 23 \[ \int (-1+\log (2)) \, dx=6-e^3-x+x^3+x \left (-x^2+\log (2)\right ) \]

[Out]

6-x-exp(3)+(ln(2)-x^2)*x+x^3

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \[ \int (-1+\log (2)) \, dx=-x (1-\log (2)) \]

[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{align*} \text {integral}& = -x (1-\log (2)) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.35 \[ \int (-1+\log (2)) \, dx=-x+x \log (2) \]

[In]

Integrate[-1 + Log[2],x]

[Out]

-x + x*Log[2]

Maple [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.30

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

[In]

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

[Out]

x*(ln(2)-1)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.35 \[ \int (-1+\log (2)) \, dx=x \log \left (2\right ) - x \]

[In]

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

[Out]

x*log(2) - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.22 \[ \int (-1+\log (2)) \, dx=x \left (-1 + \log {\left (2 \right )}\right ) \]

[In]

integrate(ln(2)-1,x)

[Out]

x*(-1 + log(2))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.26 \[ \int (-1+\log (2)) \, dx=x {\left (\log \left (2\right ) - 1\right )} \]

[In]

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

[Out]

x*(log(2) - 1)

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.26 \[ \int (-1+\log (2)) \, dx=x {\left (\log \left (2\right ) - 1\right )} \]

[In]

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

[Out]

x*(log(2) - 1)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.26 \[ \int (-1+\log (2)) \, dx=x\,\left (\ln \left (2\right )-1\right ) \]

[In]

int(log(2) - 1,x)

[Out]

x*(log(2) - 1)