\(\int 2^{\log (x)} \, dx\) [236]

Optimal result

Integrand size = 4, antiderivative size = 13 \[ \int 2^{\log (x)} \, dx=\frac {x^{1+\log (2)}}{1+\log (2)} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2306, 30} \[ \int 2^{\log (x)} \, dx=\frac {x^{1+\log (2)}}{1+\log (2)} \]

[In]

Int[2^Log[x],x]

[Out]

x^(1 + Log[2])/(1 + 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^{\log (2)} \, dx \\ & = \frac {x^{1+\log (2)}}{1+\log (2)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int 2^{\log (x)} \, dx=\frac {2^{\log (x)} x}{1+\log (2)} \]

[In]

Integrate[2^Log[x],x]

[Out]

(2^Log[x]*x)/(1 + Log[2])

Maple [A] (verified)

Time = 0.12 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00

method	result	size
gosper	\(\frac {x 2^{\ln \left (x \right )}}{1+\ln \left (2\right )}\)	\(13\)
risch	\(\frac {x \,x^{\ln \left (2\right )}}{1+\ln \left (2\right )}\)	\(13\)
parallelrisch	\(\frac {x 2^{\ln \left (x \right )}}{1+\ln \left (2\right )}\)	\(13\)
norman	\(\frac {x \,{\mathrm e}^{\ln \left (2\right ) \ln \left (x \right )}}{1+\ln \left (2\right )}\)	\(15\)

[In]

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

[Out]

x/(1+ln(2))*2^ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.35 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int 2^{\log (x)} \, dx=\frac {x e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right ) + 1} \]

[In]

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

[Out]

x*e^(log(2)*log(x))/(log(2) + 1)

Sympy [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int 2^{\log (x)} \, dx=\frac {2^{\log {\left (x \right )}} x}{\log {\left (2 \right )} + 1} \]

[In]

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

[Out]

2**log(x)*x/(log(2) + 1)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.85 \[ \int 2^{\log (x)} \, dx=\frac {2^{{\left (\frac {1}{\log \left (2\right )} + 1\right )} \log \left (x\right )}}{{\left (\frac {1}{\log \left (2\right )} + 1\right )} \log \left (2\right )} \]

[In]

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

[Out]

2^((1/log(2) + 1)*log(x))/((1/log(2) + 1)*log(2))

Giac [A] (verification not implemented)

none

Time = 0.48 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int 2^{\log (x)} \, dx=\frac {x e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right ) + 1} \]

[In]

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

[Out]

x*e^(log(2)*log(x))/(log(2) + 1)

Mupad [B] (verification not implemented)

Time = 1.54 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int 2^{\log (x)} \, dx=\frac {x^{\ln \left (2\right )+1}}{\ln \left (2\right )+1} \]

[In]

int(2^log(x),x)

[Out]

x^(log(2) + 1)/(log(2) + 1)