3.17.52 \(\int \frac {5}{9+e^3} \, dx\)

Optimal. Leaf size=10 \[ \frac {5 x}{9+e^3} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, 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 = {8} \begin {gather*} \frac {5 x}{9+e^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5/(9 + E^3),x]

[Out]

(5*x)/(9 + E^3)

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {5 x}{9+e^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {5 x}{9+e^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5/(9 + E^3),x]

[Out]

(5*x)/(9 + E^3)

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fricas [A]  time = 0.79, size = 9, normalized size = 0.90 \begin {gather*} \frac {5 \, x}{e^{3} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/(exp(3)+9),x, algorithm="fricas")

[Out]

5*x/(e^3 + 9)

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giac [A]  time = 0.29, size = 9, normalized size = 0.90 \begin {gather*} \frac {5 \, x}{e^{3} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/(exp(3)+9),x, algorithm="giac")

[Out]

5*x/(e^3 + 9)

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maple [A]  time = 0.02, size = 10, normalized size = 1.00

method	result	size
default	\(\frac {5 x}{{\mathrm e}^{3}+9}\)	\(10\)
norman	\(\frac {5 x}{{\mathrm e}^{3}+9}\)	\(10\)
risch	\(\frac {5 x}{{\mathrm e}^{3}+9}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5/(exp(3)+9),x,method=_RETURNVERBOSE)

[Out]

5*x/(exp(3)+9)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.90 \begin {gather*} \frac {5 \, x}{e^{3} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/(exp(3)+9),x, algorithm="maxima")

[Out]

5*x/(e^3 + 9)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} \frac {5\,x}{{\mathrm {e}}^3+9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5/(exp(3) + 9),x)

[Out]

(5*x)/(exp(3) + 9)

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sympy [A]  time = 0.04, size = 7, normalized size = 0.70 \begin {gather*} \frac {5 x}{9 + e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5/(exp(3)+9),x)

[Out]

5*x/(9 + exp(3))

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