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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, 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 = 0.00, size = 11, normalized size = 1.00 \[ -\frac {2^{\frac {1}{x}}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.41, size = 11, normalized size = 1.00 \[ -\frac {2^{\left (\frac {1}{x}\right )}}{\log \relax (2)} \]

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)

________________________________________________________________________________________

giac [A]  time = 0.18, size = 11, normalized size = 1.00 \[ -\frac {2^{\left (\frac {1}{x}\right )}}{\log \relax (2)} \]

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)

________________________________________________________________________________________

maple [A]  time = 0.03, size = 12, normalized size = 1.09 \[ -\frac {2^{\frac {1}{x}}}{\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.99, size = 11, normalized size = 1.00 \[ -\frac {2^{\left (\frac {1}{x}\right )}}{\log \relax (2)} \]

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)

________________________________________________________________________________________

mupad [B]  time = 3.50, size = 11, normalized size = 1.00 \[ -\frac {2^{1/x}}{\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.10, size = 8, normalized size = 0.73 \[ - \frac {2^{\frac {1}{x}}}{\log {\relax (2 )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________