3.26.56 \(\int \frac {1}{7+e^{e^4}+x} \, dx\)

Optimal. Leaf size=13 \[ \log \left (\frac {1}{4} \left (7+e^{e^4}+x\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.69, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {31} \begin {gather*} \log \left (x+e^{e^4}+7\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(7 + E^E^4 + x)^(-1),x]

[Out]

Log[7 + E^E^4 + x]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\log \left (7+e^{e^4}+x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.69 \begin {gather*} \log \left (7+e^{e^4}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 + E^E^4 + x)^(-1),x]

[Out]

Log[7 + E^E^4 + x]

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fricas [A]  time = 0.56, size = 7, normalized size = 0.54 \begin {gather*} \log \left (x + e^{\left (e^{4}\right )} + 7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(exp(1)^4)+x+7),x, algorithm="fricas")

[Out]

log(x + e^(e^4) + 7)

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giac [A]  time = 0.35, size = 8, normalized size = 0.62 \begin {gather*} \log \left ({\left | x + e^{\left (e^{4}\right )} + 7 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(exp(1)^4)+x+7),x, algorithm="giac")

[Out]

log(abs(x + e^(e^4) + 7))

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maple [A]  time = 0.40, size = 8, normalized size = 0.62

method	result	size
risch	\(\ln \left ({\mathrm e}^{{\mathrm e}^{4}}+x +7\right )\)	\(8\)
default	\(\ln \left ({\mathrm e}^{{\mathrm e}^{4}}+x +7\right )\)	\(10\)
norman	\(\ln \left ({\mathrm e}^{{\mathrm e}^{4}}+x +7\right )\)	\(10\)
meijerg	\(\ln \left (1+\frac {x}{{\mathrm e}^{{\mathrm e}^{4}}+7}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(exp(exp(1)^4)+x+7),x,method=_RETURNVERBOSE)

[Out]

ln(exp(exp(4))+x+7)

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maxima [A]  time = 0.49, size = 7, normalized size = 0.54 \begin {gather*} \log \left (x + e^{\left (e^{4}\right )} + 7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(exp(1)^4)+x+7),x, algorithm="maxima")

[Out]

log(x + e^(e^4) + 7)

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mupad [B]  time = 0.03, size = 7, normalized size = 0.54 \begin {gather*} \ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^4}+7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x + exp(exp(4)) + 7),x)

[Out]

log(x + exp(exp(4)) + 7)

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sympy [A]  time = 0.06, size = 8, normalized size = 0.62 \begin {gather*} \log {\left (x + 7 + e^{e^{4}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(exp(1)**4)+x+7),x)

[Out]

log(x + 7 + exp(exp(4)))

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