3.17.52 $\int \frac{5}{9+e^3}dx$

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

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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} $$\begin{array}{c}\frac{5x}{9+e^3}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{5x}{9+e^3}\end{array}\end{array}$$

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

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 $$\begin{array}{c}\frac{5x}{e^3+9}\end{array}$$

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 $$\begin{array}{c}\frac{5x}{e^3+9}\end{array}$$

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	$\frac{5x}{{\mathrm{e}}^3+9}$	$10$
norman	$\frac{5x}{{\mathrm{e}}^3+9}$	$10$
risch	$\frac{5x}{{\mathrm{e}}^3+9}$	$10$

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 $$\begin{array}{c}\frac{5x}{e^3+9}\end{array}$$

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 $$\begin{array}{c}\frac{5x}{{\mathrm{e}}^3+9}\end{array}$$

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 $$\begin{array}{c}\frac{5x}{9+e^3}\end{array}$$

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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