3.73.45 \(\int \frac {1}{5} \sqrt [10]{3} \sqrt [10]{e^{2 x}} \, dx\)

Optimal. Leaf size=15 \[ \sqrt [10]{3} \sqrt [10]{e^{2 x}} \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} \sqrt [10]{3} \sqrt [10]{e^{2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3^(1/10)*(E^(2*x))^(1/10))/5,x]

[Out]

3^(1/10)*(E^(2*x))^(1/10)

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 {1}{5} \sqrt [10]{3} \int \sqrt [10]{e^{2 x}} \, dx\\ &=\sqrt [10]{3} \sqrt [10]{e^{2 x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \sqrt [10]{3} \sqrt [10]{e^{2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3^(1/10)*(E^(2*x))^(1/10))/5,x]

[Out]

3^(1/10)*(E^(2*x))^(1/10)

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fricas [A]  time = 1.02, size = 8, normalized size = 0.53 \begin {gather*} 3^{\frac {1}{10}} e^{\left (\frac {1}{5} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(3^(1/2)*exp(2*x)^(1/2))^(1/5),x, algorithm="fricas")

[Out]

3^(1/10)*e^(1/5*x)

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giac [A]  time = 0.18, size = 8, normalized size = 0.53 \begin {gather*} 3^{\frac {1}{10}} e^{\left (\frac {1}{5} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(3^(1/2)*exp(2*x)^(1/2))^(1/5),x, algorithm="giac")

[Out]

3^(1/10)*e^(1/5*x)

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maple [A]  time = 0.01, size = 13, normalized size = 0.87

method	result	size
gosper	\(\left (\sqrt {3}\, \sqrt {{\mathrm e}^{2 x}}\right )^{\frac {1}{5}}\)	\(13\)
derivativedivides	\(\left (\sqrt {3}\, \sqrt {{\mathrm e}^{2 x}}\right )^{\frac {1}{5}}\)	\(13\)
default	\(\left (\sqrt {3}\, \sqrt {{\mathrm e}^{2 x}}\right )^{\frac {1}{5}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*(3^(1/2)*exp(2*x)^(1/2))^(1/5),x,method=_RETURNVERBOSE)

[Out]

(3^(1/2)*exp(2*x)^(1/2))^(1/5)

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maxima [A]  time = 0.45, size = 8, normalized size = 0.53 \begin {gather*} 3^{\frac {1}{10}} e^{\left (\frac {1}{5} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(3^(1/2)*exp(2*x)^(1/2))^(1/5),x, algorithm="maxima")

[Out]

3^(1/10)*e^(1/5*x)

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mupad [B]  time = 0.07, size = 8, normalized size = 0.53 \begin {gather*} 3^{1/10}\,{\mathrm {e}}^{x/5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3^(1/2)*exp(2*x)^(1/2))^(1/5)/5,x)

[Out]

3^(1/10)*exp(x/5)

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sympy [A]  time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} \sqrt [10]{3} \sqrt [10]{e^{2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(3**(1/2)*exp(2*x)**(1/2))**(1/5),x)

[Out]

3**(1/10)*exp(2*x)**(1/10)

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