3.8.39 \(\int \frac {2^{\frac {1}{x}}}{x^2} \, dx\) [739]

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

[Out]

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

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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 = {2240} \begin {gather*} -\frac {2^{\frac {1}{x}}}{\log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 2240

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*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2^{\frac {1}{x}}}{\log (2)} \end {gather*}

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 = 0.02, size = 12, normalized size = 1.09

method	result	size
gosper	\(-\frac {2^{\frac {1}{x}}}{\ln \left (2\right )}\)	\(12\)
derivativedivides	\(-\frac {2^{\frac {1}{x}}}{\ln \left (2\right )}\)	\(12\)
default	\(-\frac {2^{\frac {1}{x}}}{\ln \left (2\right )}\)	\(12\)
risch	\(-\frac {2^{\frac {1}{x}}}{\ln \left (2\right )}\)	\(12\)
norman	\(-\frac {{\mathrm e}^{\frac {\ln \left (2\right )}{x}}}{\ln \left (2\right )}\)	\(14\)
meijerg	\(\frac {1-{\mathrm e}^{\frac {\ln \left (2\right )}{x}}}{\ln \left (2\right )}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^(1/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.28, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2^{\left (\frac {1}{x}\right )}}{\log \left (2\right )} \end {gather*}

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 = 0.38, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2^{\left (\frac {1}{x}\right )}}{\log \left (2\right )} \end {gather*}

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 = 0.03, size = 8, normalized size = 0.73 \begin {gather*} - \frac {2^{\frac {1}{x}}}{\log {\left (2 \right )}} \end {gather*}

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 = 4.62, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2^{\left (\frac {1}{x}\right )}}{\log \left (2\right )} \end {gather*}

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)

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Mupad [B]
time = 3.50, size = 11, normalized size = 1.00 \begin {gather*} -\frac {2^{1/x}}{\ln \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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