\(\int \frac {5}{9+e^3} \, dx\) [1652]

Optimal result

Integrand size = 9, antiderivative size = 10 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 x}{9+e^3} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \[ \int \frac {5}{9+e^3} \, dx=\frac {5 x}{9+e^3} \]

[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{align*} \text {integral}& = \frac {5 x}{9+e^3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 x}{9+e^3} \]

[In]

Integrate[5/(9 + E^3),x]

[Out]

(5*x)/(9 + E^3)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 \, x}{e^{3} + 9} \]

[In]

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

[Out]

5*x/(e^3 + 9)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 x}{9 + e^{3}} \]

[In]

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

[Out]

5*x/(9 + exp(3))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 \, x}{e^{3} + 9} \]

[In]

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

[Out]

5*x/(e^3 + 9)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {5}{9+e^3} \, dx=\frac {5 \, x}{e^{3} + 9} \]

[In]

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

[Out]

5*x/(e^3 + 9)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {5}{9+e^3} \, dx=\frac {5\,x}{{\mathrm {e}}^3+9} \]

[In]

int(5/(exp(3) + 9),x)

[Out]

(5*x)/(exp(3) + 9)