3.1912 \(\int (\frac{1}{2 \sqrt{x}}+2 \sqrt{x}) \, dx\)

Optimal. Leaf size=15 \[ \frac{4 x^{3/2}}{3}+\sqrt{x} \]

[Out]

Sqrt[x] + (4*x^(3/2))/3

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Rubi [A]  time = 0.0013879, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{4 x^{3/2}}{3}+\sqrt{x} \]

Antiderivative was successfully verified.

[In]

Int[1/(2*Sqrt[x]) + 2*Sqrt[x],x]

[Out]

Sqrt[x] + (4*x^(3/2))/3

Rubi steps

\begin{align*} \int \left (\frac{1}{2 \sqrt{x}}+2 \sqrt{x}\right ) \, dx &=\sqrt{x}+\frac{4 x^{3/2}}{3}\\ \end{align*}

Mathematica [A]  time = 0.0034131, size = 14, normalized size = 0.93 \[ \frac{1}{3} \sqrt{x} (4 x+3) \]

Antiderivative was successfully verified.

[In]

Integrate[1/(2*Sqrt[x]) + 2*Sqrt[x],x]

[Out]

(Sqrt[x]*(3 + 4*x))/3

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Maple [A]  time = 0.002, size = 11, normalized size = 0.7 \begin{align*}{\frac{4\,x+3}{3}\sqrt{x}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2/x^(1/2)+2*x^(1/2),x)

[Out]

1/3*x^(1/2)*(4*x+3)

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Maxima [A]  time = 0.965711, size = 12, normalized size = 0.8 \begin{align*} \frac{4}{3} \, x^{\frac{3}{2}} + \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4/3*x^(3/2) + sqrt(x)

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Fricas [A]  time = 2.12502, size = 31, normalized size = 2.07 \begin{align*} \frac{1}{3} \,{\left (4 \, x + 3\right )} \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*(4*x + 3)*sqrt(x)

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Sympy [A]  time = 0.054219, size = 12, normalized size = 0.8 \begin{align*} \frac{4 x^{\frac{3}{2}}}{3} + \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x**(3/2)/3 + sqrt(x)

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Giac [A]  time = 1.04754, size = 12, normalized size = 0.8 \begin{align*} \frac{4}{3} \, x^{\frac{3}{2}} + \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4/3*x^(3/2) + sqrt(x)