3.84.97 \(\int \frac {2-e^4}{x} \, dx\) [8397]

Optimal. Leaf size=16 \[ -\frac {1}{8}+\left (2-e^4\right ) \log (5 x) \]

[Out]

(2-exp(4))*ln(5*x)-1/8

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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.62, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 29} \begin {gather*} \left (2-e^4\right ) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 - E^4)/x,x]

[Out]

(2 - E^4)*Log[x]

Rule 12

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

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (2-e^4\right ) \int \frac {1}{x} \, dx\\ &=\left (2-e^4\right ) \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.62 \begin {gather*} \left (2-e^4\right ) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 - E^4)/x,x]

[Out]

(2 - E^4)*Log[x]

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Maple [A]
time = 0.20, size = 10, normalized size = 0.62

method	result	size
default	\(\left (2-{\mathrm e}^{4}\right ) \ln \left (x \right )\)	\(10\)
norman	\(\left (2-{\mathrm e}^{4}\right ) \ln \left (x \right )\)	\(10\)
risch	\(-{\mathrm e}^{4} \ln \left (x \right )+2 \ln \left (x \right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2-exp(4))/x,x,method=_RETURNVERBOSE)

[Out]

(2-exp(4))*ln(x)

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Maxima [A]
time = 0.36, size = 8, normalized size = 0.50 \begin {gather*} -{\left (e^{4} - 2\right )} \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2-exp(4))/x,x, algorithm="maxima")

[Out]

-(e^4 - 2)*log(x)

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Fricas [A]
time = 0.39, size = 8, normalized size = 0.50 \begin {gather*} -{\left (e^{4} - 2\right )} \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2-exp(4))/x,x, algorithm="fricas")

[Out]

-(e^4 - 2)*log(x)

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Sympy [A]
time = 0.01, size = 7, normalized size = 0.44 \begin {gather*} \left (2 - e^{4}\right ) \log {\left (x \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2-exp(4))/x,x)

[Out]

(2 - exp(4))*log(x)

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Giac [A]
time = 0.39, size = 9, normalized size = 0.56 \begin {gather*} -{\left (e^{4} - 2\right )} \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2-exp(4))/x,x, algorithm="giac")

[Out]

-(e^4 - 2)*log(abs(x))

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Mupad [B]
time = 5.71, size = 8, normalized size = 0.50 \begin {gather*} -\ln \left (x\right )\,\left ({\mathrm {e}}^4-2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(4) - 2)/x,x)

[Out]

-log(x)*(exp(4) - 2)

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