3.90.64 \(\int \frac {1}{7+e^{64}} \, dx\)

Optimal. Leaf size=9 \[ \frac {x}{7+e^{64}} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} \frac {x}{7+e^{64}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(7 + E^64)^(-1),x]

[Out]

x/(7 + E^64)

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{7+e^{64}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{7+e^{64}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 + E^64)^(-1),x]

[Out]

x/(7 + E^64)

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fricas [A]  time = 0.45, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{64} + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(64)+7),x, algorithm="fricas")

[Out]

x/(e^64 + 7)

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giac [A]  time = 0.15, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{64} + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(64)+7),x, algorithm="giac")

[Out]

x/(e^64 + 7)

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maple [A]  time = 0.02, size = 9, normalized size = 1.00

method	result	size
default	\(\frac {x}{{\mathrm e}^{64}+7}\)	\(9\)
norman	\(\frac {x}{{\mathrm e}^{64}+7}\)	\(9\)
risch	\(\frac {x}{{\mathrm e}^{64}+7}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(exp(64)+7),x,method=_RETURNVERBOSE)

[Out]

x/(exp(64)+7)

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maxima [A]  time = 0.35, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{64} + 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(64)+7),x, algorithm="maxima")

[Out]

x/(e^64 + 7)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{{\mathrm {e}}^{64}+7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(exp(64) + 7),x)

[Out]

x/(exp(64) + 7)

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sympy [A]  time = 0.04, size = 5, normalized size = 0.56 \begin {gather*} \frac {x}{7 + e^{64}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(64)+7),x)

[Out]

x/(7 + exp(64))

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