\(\int -\frac {2 x}{\log (2)} \, dx\) [7572]

Optimal result

Integrand size = 7, antiderivative size = 25 \[ \int -\frac {2 x}{\log (2)} \, dx=\frac {1+e^3-e^5-\frac {x+x^3}{x}}{\log (2)} \]

[Out]

(exp(3)-1/x*(x^3+x)+1-exp(5))/ln(2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30} \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^2}{\log (2)} \]

[In]

Int[(-2*x)/Log[2],x]

[Out]

-(x^2/Log[2])

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = -\frac {2 \int x \, dx}{\log (2)} \\ & = -\frac {x^2}{\log (2)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36 \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^2}{\log (2)} \]

[In]

Integrate[(-2*x)/Log[2],x]

[Out]

-(x^2/Log[2])

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.40

method	result	size
gosper	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)
default	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)
norman	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)
risch	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)
parallelrisch	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)

[In]

int(-2*x/ln(2),x,method=_RETURNVERBOSE)

[Out]

-x^2/ln(2)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36 \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^{2}}{\log \left (2\right )} \]

[In]

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

[Out]

-x^2/log(2)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.28 \[ \int -\frac {2 x}{\log (2)} \, dx=- \frac {x^{2}}{\log {\left (2 \right )}} \]

[In]

integrate(-2*x/ln(2),x)

[Out]

-x**2/log(2)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36 \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^{2}}{\log \left (2\right )} \]

[In]

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

[Out]

-x^2/log(2)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36 \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^{2}}{\log \left (2\right )} \]

[In]

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

[Out]

-x^2/log(2)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.36 \[ \int -\frac {2 x}{\log (2)} \, dx=-\frac {x^2}{\ln \left (2\right )} \]

[In]

int(-(2*x)/log(2),x)

[Out]

-x^2/log(2)