3.20.12 \(\int (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}) \, dx\) [1912]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {4 x^{3/2}}{3}+\sqrt {x} \end {gather*}

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*}

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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.93 \begin {gather*} \frac {1}{3} \sqrt {x} (3+4 x) \end {gather*}

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 = 0.02, size = 10, normalized size = 0.67

method	result	size
derivativedivides	\(\frac {4 x^{\frac {3}{2}}}{3}+\sqrt {x}\)	\(10\)
default	\(\frac {4 x^{\frac {3}{2}}}{3}+\sqrt {x}\)	\(10\)
risch	\(\frac {4 x^{\frac {3}{2}}}{3}+\sqrt {x}\)	\(10\)
gosper	\(\frac {\sqrt {x}\, \left (3+4 x \right )}{3}\)	\(11\)
trager	\(\frac {\left (2+\frac {8 x}{3}\right ) \sqrt {x}}{2}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.27, size = 9, normalized size = 0.60 \begin {gather*} \frac {4}{3} \, x^{\frac {3}{2}} + \sqrt {x} \end {gather*}

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 = 0.80, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{3} \, {\left (4 \, x + 3\right )} \sqrt {x} \end {gather*}

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 = 0.01, size = 12, normalized size = 0.80 \begin {gather*} \frac {4 x^{\frac {3}{2}}}{3} + \sqrt {x} \end {gather*}

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 = 1.36, size = 9, normalized size = 0.60 \begin {gather*} \frac {4}{3} \, x^{\frac {3}{2}} + \sqrt {x} \end {gather*}

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)

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Mupad [B]
time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} \frac {\sqrt {x}\,\left (4\,x+3\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(2*x^(1/2)) + 2*x^(1/2),x)

[Out]

(x^(1/2)*(4*x + 3))/3

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