\(\int \frac {2^{\log (x)}}{x} \, dx\) [139]

Optimal result

Integrand size = 8, antiderivative size = 9 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {2^{\log (x)}}{\log (2)} \]

[Out]

2^ln(x)/ln(2)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2306, 30} \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {x^{\log (2)}}{\log (2)} \]

[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 2306

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

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {2^{\log (x)}}{\log (2)} \]

[In]

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

[Out]

2^Log[x]/Log[2]

Maple [A] (verified)

Time = 0.40 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11

method	result	size
gosper	\(\frac {2^{\ln \left (x \right )}}{\ln \left (2\right )}\)	\(10\)
derivativedivides	\(\frac {2^{\ln \left (x \right )}}{\ln \left (2\right )}\)	\(10\)
default	\(\frac {2^{\ln \left (x \right )}}{\ln \left (2\right )}\)	\(10\)
risch	\(\frac {x^{\ln \left (2\right )}}{\ln \left (2\right )}\)	\(10\)
parallelrisch	\(\frac {2^{\ln \left (x \right )}}{\ln \left (2\right )}\)	\(10\)
norman	\(\frac {{\mathrm e}^{\ln \left (2\right ) \ln \left (x \right )}}{\ln \left (2\right )}\)	\(12\)

[In]

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

[Out]

2^ln(x)/ln(2)

Fricas [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right )} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {2^{\log {\left (x \right )}}}{\log {\left (2 \right )}} \]

[In]

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

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {2^{\log \left (x\right )}}{\log \left (2\right )} \]

[In]

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

[Out]

2^log(x)/log(2)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {2^{\log \left (x\right )}}{\log \left (2\right )} \]

[In]

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

[Out]

2^log(x)/log(2)

Mupad [B] (verification not implemented)

Time = 1.45 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\log (x)}}{x} \, dx=\frac {x^{\ln \left (2\right )}}{\ln \left (2\right )} \]

[In]

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

[Out]

x^log(2)/log(2)