3.8.43 \(\int \frac {10^{\sqrt {x}}}{\sqrt {x}} \, dx\) [743]

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

[Out]

2^(1+x^(1/2))*5^(x^(1/2))/ln(10)

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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, 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 = {2240} \begin {gather*} \frac {2^{\sqrt {x}+1} 5^{\sqrt {x}}}{\log (10)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2^(1 + Sqrt[x])*5^Sqrt[x])/Log[10]

Rule 2240

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*}

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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} \frac {2^{1+\sqrt {x}} 5^{\sqrt {x}}}{\log (10)} \end {gather*}

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 = 0.03, size = 12, normalized size = 0.57

method	result	size
derivativedivides	\(\frac {2 \,10^{\sqrt {x}}}{\ln \left (10\right )}\)	\(12\)
default	\(\frac {2 \,10^{\sqrt {x}}}{\ln \left (10\right )}\)	\(12\)
meijerg	\(-\frac {2 \left (1-{\mathrm e}^{\sqrt {x}\, \ln \left (10\right )}\right )}{\ln \left (10\right )}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10^(x^(1/2))/x^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.30, size = 11, normalized size = 0.52 \begin {gather*} \frac {2 \cdot 10^{\left (\sqrt {x}\right )}}{\log \left (10\right )} \end {gather*}

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 = 0.35, size = 11, normalized size = 0.52 \begin {gather*} \frac {2 \cdot 10^{\left (\sqrt {x}\right )}}{\log \left (10\right )} \end {gather*}

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 = 0.05, size = 10, normalized size = 0.48 \begin {gather*} \frac {2 \cdot 10^{\sqrt {x}}}{\log {\left (10 \right )}} \end {gather*}

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 = 5.04, size = 11, normalized size = 0.52 \begin {gather*} \frac {2 \cdot 10^{\left (\sqrt {x}\right )}}{\log \left (10\right )} \end {gather*}

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)

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Mupad [B]
time = 3.49, size = 11, normalized size = 0.52 \begin {gather*} \frac {2\,{10}^{\sqrt {x}}}{\ln \left (10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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