3.139 \(\int \frac {2^{\log (x)}}{x} \, dx\)

Optimal. Leaf size=9 \[ \frac {2^{\log (x)}}{\log (2)} \]

[Out]

2^ln(x)/ln(2)

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Rubi [A]  time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2274, 30} \[ \frac {x^{\log (2)}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

Int[2^Log[x]/x,x]

[Out]

x^Log[2]/Log[2]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 2274

Int[(u_.)*(F_)^((a_.)*(Log[z_]*(b_.) + (v_.))), x_Symbol] :> Int[u*F^(a*v)*z^(a*b*Log[F]), x] /; FreeQ[{F, a,
b}, x]

Rubi steps

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

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Mathematica [A]  time = 0.01, size = 9, normalized size = 1.00 \[ \frac {2^{\log (x)}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

Integrate[2^Log[x]/x,x]

[Out]

2^Log[x]/Log[2]

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fricas [A]  time = 0.85, size = 11, normalized size = 1.22 \[ \frac {e^{\left (\log \relax (2) \log \relax (x)\right )}}{\log \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(log(2)*log(x))/log(2)

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giac [A]  time = 0.18, size = 9, normalized size = 1.00 \[ \frac {2^{\log \relax (x)}}{\log \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2^log(x)/log(2)

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maple [A]  time = 0.07, size = 10, normalized size = 1.11 \[ \frac {2^{\ln \relax (x )}}{\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2^ln(x)/ln(2)

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maxima [A]  time = 0.58, size = 9, normalized size = 1.00 \[ \frac {2^{\log \relax (x)}}{\log \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2^log(x)/log(2)

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mupad [B]  time = 0.40, size = 9, normalized size = 1.00 \[ \frac {x^{\ln \relax (2)}}{\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^log(2)/log(2)

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sympy [A]  time = 0.38, size = 7, normalized size = 0.78 \[ \frac {2^{\log {\relax (x )}}}{\log {\relax (2 )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2**log(x)/log(2)

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