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

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

[Out]

x^(1 + Log[2])/(1 + Log[2])

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Rubi [A]  time = 0.0054808, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, 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 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]

Rule 30

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

Rubi steps

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

Mathematica [A]  time = 0.0025823, 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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Maple [A]  time = 0.013, size = 13, normalized size = 1. \begin{align*}{\frac{x{2}^{\ln \left ( x \right ) }}{1+\ln \left ( 2 \right ) }} \end{align*}

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 = 1.02621, size = 32, normalized size = 2.46 \begin{align*} \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 )} \end{align*}

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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Fricas [A]  time = 1.89423, size = 46, normalized size = 3.54 \begin{align*} \frac{x e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right ) + 1} \end{align*}

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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Sympy [A]  time = 0.417882, size = 10, normalized size = 0.77 \begin{align*} \frac{2^{\log{\left (x \right )}} x}{\log{\left (2 \right )} + 1} \end{align*}

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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Giac [A]  time = 1.2181, size = 19, normalized size = 1.46 \begin{align*} \frac{x e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right ) + 1} \end{align*}

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)