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

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

[Out]

2^Log[x]/Log

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Rubi [A]  time = 0.0154783, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0.25, Rules used = {2274, 30} $\frac{x^{\log (2)}}{\log (2)}$

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

x^Log/Log

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

Mathematica [A]  time = 0.0064506, size = 9, normalized size = 1. $\frac{2^{\log (x)}}{\log (2)}$

Antiderivative was successfully veriﬁed.

[In]

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

[Out]

2^Log[x]/Log

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Maple [A]  time = 0.013, size = 10, normalized size = 1.1 \begin{align*}{\frac{{2}^{\ln \left ( x \right ) }}{\ln \left ( 2 \right ) }} \end{align*}

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 = 1.07262, size = 12, normalized size = 1.33 \begin{align*} \frac{2^{\log \left (x\right )}}{\log \left (2\right )} \end{align*}

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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Fricas [A]  time = 2.14421, size = 35, normalized size = 3.89 \begin{align*} \frac{e^{\left (\log \left (2\right ) \log \left (x\right )\right )}}{\log \left (2\right )} \end{align*}

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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Sympy [A]  time = 0.418147, size = 7, normalized size = 0.78 \begin{align*} \frac{2^{\log{\left (x \right )}}}{\log{\left (2 \right )}} \end{align*}

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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Giac [A]  time = 1.29955, size = 12, normalized size = 1.33 \begin{align*} \frac{2^{\log \left (x\right )}}{\log \left (2\right )} \end{align*}

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)