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

Optimal. Leaf size=11 \[ \frac {3}{64} e^{2 x/25} \]

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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 {gather*} \frac {3}{64} e^{2 x/25} \end {gather*}

Antiderivative was successfully verified.

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

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {3}{64} e^{2 x/25} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [A]  time = 0.60, size = 6, normalized size = 0.55 \begin {gather*} \frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.22, size = 6, normalized size = 0.55 \begin {gather*} \frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.02, size = 7, normalized size = 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	\(-\frac {3}{64}+\frac {3 \,{\mathrm e}^{\frac {2 x}{25}}}{64}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.44, size = 6, normalized size = 0.55 \begin {gather*} \frac {3}{64} \, e^{\left (\frac {2}{25} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 0.02, size = 6, normalized size = 0.55 \begin {gather*} \frac {3\,{\mathrm {e}}^{\frac {2\,x}{25}}}{64} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.04, size = 8, normalized size = 0.73 \begin {gather*} \frac {3 e^{\frac {2 x}{25}}}{64} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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