\(\int \frac {3}{800} e^{2 x/25} \, dx\) [1021]

Optimal result

Integrand size = 11, antiderivative size = 11 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} e^{2 x/25} \]

[Out]

3/64*exp(1/25*x)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2225} \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} e^{2 x/25} \]

[In]

Int[(3*E^((2*x)/25))/800,x]

[Out]

(3*E^((2*x)/25))/64

Rule 12

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

Rule 2225

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{align*} \text {integral}& = \frac {3}{800} \int e^{2 x/25} \, dx \\ & = \frac {3}{64} e^{2 x/25} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} e^{2 x/25} \]

[In]

Integrate[(3*E^((2*x)/25))/800,x]

[Out]

(3*E^((2*x)/25))/64

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64

method	result	size
risch	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(7\)
gosper	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)
derivativedivides	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)
default	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)
norman	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)
meijerg	\(-\frac {3}{64}+\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)
parallelrisch	\(\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)

[In]

int(3/800*exp(1/25*x)^2,x,method=_RETURNVERBOSE)

[Out]

3/64*exp(2/25*x)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \]

[In]

integrate(3/800*exp(1/25*x)^2,x, algorithm="fricas")

[Out]

3/64*e^(2/25*x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3 e^{\frac {2 x}{25}}}{64} \]

[In]

integrate(3/800*exp(1/25*x)**2,x)

[Out]

3*exp(2*x/25)/64

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \]

[In]

integrate(3/800*exp(1/25*x)^2,x, algorithm="maxima")

[Out]

3/64*e^(2/25*x)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \]

[In]

integrate(3/800*exp(1/25*x)^2,x, algorithm="giac")

[Out]

3/64*e^(2/25*x)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {3}{800} e^{2 x/25} \, dx=\frac {3\,{\mathrm {e}}^{\frac {2\,x}{25}}}{64} \]

[In]

int((3*exp((2*x)/25))/800,x)

[Out]

(3*exp((2*x)/25))/64