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

Optimal. Leaf size=13 \[ \frac {x^{1+\log (2)}}{1+\log (2)} \]

[Out]

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

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2274, 30} \[ \frac {x^{1+\log (2)}}{1+\log (2)} \]

Antiderivative was successfully verified.

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

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.92 \[ \frac {x 2^{\log (x)}}{1+\log (2)} \]

Antiderivative was successfully verified.

[In]

Integrate[2^Log[x],x]

[Out]

(2^Log[x]*x)/(1 + Log[2])

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fricas [A]  time = 0.43, size = 14, normalized size = 1.08 \[ \frac {x e^{\left (\log \relax (2) \log \relax (x)\right )}}{\log \relax (2) + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e^(log(2)*log(x))/(log(2) + 1)

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giac [A]  time = 0.16, size = 14, normalized size = 1.08 \[ \frac {x e^{\left (\log \relax (2) \log \relax (x)\right )}}{\log \relax (2) + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e^(log(2)*log(x))/(log(2) + 1)

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maple [A]  time = 0.06, size = 13, normalized size = 1.00 \[ \frac {x 2^{\ln \relax (x )}}{1+\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^ln(x),x)

[Out]

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

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maxima [A]  time = 0.52, size = 24, normalized size = 1.85 \[ \frac {2^{{\left (\frac {1}{\log \relax (2)} + 1\right )} \log \relax (x)}}{{\left (\frac {1}{\log \relax (2)} + 1\right )} \log \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 0.36, size = 13, normalized size = 1.00 \[ \frac {x^{\ln \relax (2)+1}}{\ln \relax (2)+1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^log(x),x)

[Out]

x^(log(2) + 1)/(log(2) + 1)

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sympy [A]  time = 0.39, size = 10, normalized size = 0.77 \[ \frac {2^{\log {\relax (x )}} x}{\log {\relax (2 )} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2**log(x)*x/(log(2) + 1)

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