3.73.9 $\int \frac{8}{15}{e}^{4x/3}dx$

Optimal. Leaf size=11 $$\frac{2}{5}{e}^{4x/3}$$

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.182, Rules used = {12, 2194} $$\begin{array}{c}\frac{2}{5}{e}^{4x/3}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(8*E^((4*x)/3))/15,x]

[Out]

(2*E^((4*x)/3))/5

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{8}{15}\int e^{4x/3}dx\\ & =\frac{2}{5}{e}^{4x/3}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 $$\begin{array}{c}\frac{2}{5}{e}^{4x/3}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(8*E^((4*x)/3))/15,x]

[Out]

(2*E^((4*x)/3))/5

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fricas [A]  time = 1.14, size = 6, normalized size = 0.55 $$\begin{array}{c}\frac{2}{5}{e}^{\left(\frac{4}{3}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8/15*exp(4/3*x),x, algorithm="fricas")

[Out]

2/5*e^(4/3*x)

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giac [A]  time = 0.22, size = 6, normalized size = 0.55 $$\begin{array}{c}\frac{2}{5}{e}^{\left(\frac{4}{3}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8/15*exp(4/3*x),x, algorithm="giac")

[Out]

2/5*e^(4/3*x)

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maple [A]  time = 0.02, size = 7, normalized size = 0.64

method	result	size
gosper	$\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$7$
derivativedivides	$\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$7$
default	$\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$7$
norman	$\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$7$
risch	$\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$7$
meijerg	$-\frac{2}{5}+\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}$	$9$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8/15*exp(4/3*x),x,method=_RETURNVERBOSE)

[Out]

2/5*exp(4/3*x)

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maxima [A]  time = 0.35, size = 6, normalized size = 0.55 $$\begin{array}{c}\frac{2}{5}{e}^{\left(\frac{4}{3}x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8/15*exp(4/3*x),x, algorithm="maxima")

[Out]

2/5*e^(4/3*x)

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mupad [B]  time = 0.02, size = 6, normalized size = 0.55 $$\begin{array}{c}\frac{2{\mathrm{e}}^{\frac{4x}{3}}}{5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*exp((4*x)/3))/15,x)

[Out]

(2*exp((4*x)/3))/5

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sympy [A]  time = 0.05, size = 8, normalized size = 0.73 $$\begin{array}{c}\frac{2e^{\frac{4x}{3}}}{5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8/15*exp(4/3*x),x)

[Out]

2*exp(4*x/3)/5

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