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

Optimal. Leaf size=25 \[ \frac {1+e^3-e^5-\frac {x+x^3}{x}}{\log (2)} \]

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.36, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30} \begin {gather*} -\frac {x^2}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=-\frac {2 \int x \, dx}{\log (2)}\\ &=-\frac {x^2}{\log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^2}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-(x^2/Log[2])

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Maple [A]
time = 0.37, size = 10, normalized size = 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	\(-\frac {x^{2}}{\ln \left (2\right )}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^2/ln(2)

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Maxima [A]
time = 0.27, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^2/log(2)

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Fricas [A]
time = 0.36, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^2/log(2)

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Sympy [A]
time = 0.01, size = 7, normalized size = 0.28 \begin {gather*} - \frac {x^{2}}{\log {\left (2 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x**2/log(2)

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Giac [A]
time = 0.43, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^2/log(2)

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Mupad [B]
time = 0.04, size = 9, normalized size = 0.36 \begin {gather*} -\frac {x^2}{\ln \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^2/log(2)

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