3.743 \(\int \frac{10^{\sqrt{x}}}{\sqrt{x}} \, dx\)

Optimal. Leaf size=21 \[ \frac{2^{\sqrt{x}+1} 5^{\sqrt{x}}}{\log (10)} \]

[Out]

(2^(1 + Sqrt[x])*5^Sqrt[x])/Log[10]

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Rubi [A]  time = 0.0114011, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2209} \[ \frac{2^{\sqrt{x}+1} 5^{\sqrt{x}}}{\log (10)} \]

Antiderivative was successfully verified.

[In]

Int[10^Sqrt[x]/Sqrt[x],x]

[Out]

(2^(1 + Sqrt[x])*5^Sqrt[x])/Log[10]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin{align*} \int \frac{10^{\sqrt{x}}}{\sqrt{x}} \, dx &=\frac{2^{1+\sqrt{x}} 5^{\sqrt{x}}}{\log (10)}\\ \end{align*}

Mathematica [A]  time = 0.0028632, size = 21, normalized size = 1. \[ \frac{2^{\sqrt{x}+1} 5^{\sqrt{x}}}{\log (10)} \]

Antiderivative was successfully verified.

[In]

Integrate[10^Sqrt[x]/Sqrt[x],x]

[Out]

(2^(1 + Sqrt[x])*5^Sqrt[x])/Log[10]

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Maple [A]  time = 0.019, size = 12, normalized size = 0.6 \begin{align*} 2\,{\frac{{10}^{\sqrt{x}}}{\ln \left ( 10 \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10^(x^(1/2))/x^(1/2),x)

[Out]

2/ln(10)*10^(x^(1/2))

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Maxima [A]  time = 0.949181, size = 15, normalized size = 0.71 \begin{align*} \frac{2 \cdot 10^{\left (\sqrt{x}\right )}}{\log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(x^(1/2))/x^(1/2),x, algorithm="maxima")

[Out]

2*10^sqrt(x)/log(10)

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Fricas [A]  time = 0.883467, size = 30, normalized size = 1.43 \begin{align*} \frac{2 \cdot 10^{\left (\sqrt{x}\right )}}{\log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(x^(1/2))/x^(1/2),x, algorithm="fricas")

[Out]

2*10^sqrt(x)/log(10)

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Sympy [A]  time = 0.139031, size = 10, normalized size = 0.48 \begin{align*} \frac{2 \cdot 10^{\sqrt{x}}}{\log{\left (10 \right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10**(x**(1/2))/x**(1/2),x)

[Out]

2*10**(sqrt(x))/log(10)

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Giac [A]  time = 1.21473, size = 15, normalized size = 0.71 \begin{align*} \frac{2 \cdot 10^{\left (\sqrt{x}\right )}}{\log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(x^(1/2))/x^(1/2),x, algorithm="giac")

[Out]

2*10^sqrt(x)/log(10)