3.739 \(\int \frac{2^{\frac{1}{x}}}{x^2} \, dx\)

Optimal. Leaf size=11 \[ -\frac{2^{\frac{1}{x}}}{\log (2)} \]

[Out]

-(2^x^(-1)/Log[2])

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Rubi [A]  time = 0.0109216, antiderivative size = 11, normalized size of antiderivative = 1., 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 = {2209} \[ -\frac{2^{\frac{1}{x}}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

Int[2^x^(-1)/x^2,x]

[Out]

-(2^x^(-1)/Log[2])

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin{align*} \int \frac{2^{\frac{1}{x}}}{x^2} \, dx &=-\frac{2^{\frac{1}{x}}}{\log (2)}\\ \end{align*}

Mathematica [A]  time = 0.0015678, size = 11, normalized size = 1. \[ -\frac{2^{\frac{1}{x}}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

Integrate[2^x^(-1)/x^2,x]

[Out]

-(2^x^(-1)/Log[2])

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Maple [A]  time = 0.022, size = 12, normalized size = 1.1 \begin{align*} -{\frac{\sqrt [x]{2}}{\ln \left ( 2 \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^(1/x)/x^2,x)

[Out]

-2^(1/x)/ln(2)

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Maxima [A]  time = 0.97364, size = 15, normalized size = 1.36 \begin{align*} -\frac{2^{\left (\frac{1}{x}\right )}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(1/x)/x^2,x, algorithm="maxima")

[Out]

-2^(1/x)/log(2)

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Fricas [A]  time = 0.721701, size = 23, normalized size = 2.09 \begin{align*} -\frac{2^{\left (\frac{1}{x}\right )}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(1/x)/x^2,x, algorithm="fricas")

[Out]

-2^(1/x)/log(2)

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Sympy [A]  time = 0.098418, size = 8, normalized size = 0.73 \begin{align*} - \frac{2^{\frac{1}{x}}}{\log{\left (2 \right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2**(1/x)/x**2,x)

[Out]

-2**(1/x)/log(2)

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Giac [A]  time = 1.29599, size = 15, normalized size = 1.36 \begin{align*} -\frac{2^{\left (\frac{1}{x}\right )}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(1/x)/x^2,x, algorithm="giac")

[Out]

-2^(1/x)/log(2)