3.16.95 \(\int \frac {1}{3 e^{45}+x} \, dx\)

Optimal. Leaf size=8 \[ \log \left (3 e^{45}+x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {31} \begin {gather*} \log \left (x+3 e^{45}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3*E^45 + x)^(-1),x]

[Out]

Log[3*E^45 + 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 (3 e^{45}+x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \log \left (3 e^{45}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*E^45 + x)^(-1),x]

[Out]

Log[3*E^45 + x]

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fricas [A]  time = 0.79, size = 7, normalized size = 0.88 \begin {gather*} \log \left (x + 3 \, e^{45}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3*exp(45)+x),x, algorithm="fricas")

[Out]

log(x + 3*e^45)

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giac [A]  time = 0.17, size = 8, normalized size = 1.00 \begin {gather*} \log \left ({\left | x + 3 \, e^{45} \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3*exp(45)+x),x, algorithm="giac")

[Out]

log(abs(x + 3*e^45))

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maple [A]  time = 0.28, size = 8, normalized size = 1.00

method	result	size
default	\(\ln \left (3 \,{\mathrm e}^{45}+x \right )\)	\(8\)
norman	\(\ln \left (3 \,{\mathrm e}^{45}+x \right )\)	\(8\)
risch	\(\ln \left (3 \,{\mathrm e}^{45}+x \right )\)	\(8\)
meijerg	\(\ln \left (1+\frac {x \,{\mathrm e}^{-45}}{3}\right )\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(3*exp(45)+x),x,method=_RETURNVERBOSE)

[Out]

ln(3*exp(45)+x)

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maxima [A]  time = 0.37, size = 7, normalized size = 0.88 \begin {gather*} \log \left (x + 3 \, e^{45}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3*exp(45)+x),x, algorithm="maxima")

[Out]

log(x + 3*e^45)

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mupad [B]  time = 0.03, size = 7, normalized size = 0.88 \begin {gather*} \ln \left (x+3\,{\mathrm {e}}^{45}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x + 3*exp(45)),x)

[Out]

log(x + 3*exp(45))

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sympy [A]  time = 0.05, size = 7, normalized size = 0.88 \begin {gather*} \log {\left (x + 3 e^{45} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(3*exp(45)+x),x)

[Out]

log(x + 3*exp(45))

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