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

Optimal result

Integrand size = 17, antiderivative size = 15 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\sqrt {x}+\frac {4 x^{3/2}}{3} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {4 x^{3/2}}{3}+\sqrt {x} \]

[In]

Int[1/(2*Sqrt[x]) + 2*Sqrt[x],x]

[Out]

Sqrt[x] + (4*x^(3/2))/3

Rubi steps \begin{align*} \text {integral}& = \sqrt {x}+\frac {4 x^{3/2}}{3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {1}{3} \sqrt {x} (3+4 x) \]

[In]

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

[Out]

(Sqrt[x]*(3 + 4*x))/3

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 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	\(\frac {\sqrt {x}\, \left (4 x +3\right )}{3}\)	\(11\)
trager	\(\frac {\left (\frac {8 x}{3}+2\right ) \sqrt {x}}{2}\)	\(11\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {1}{3} \, {\left (4 \, x + 3\right )} \sqrt {x} \]

[In]

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

[Out]

1/3*(4*x + 3)*sqrt(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {4 x^{\frac {3}{2}}}{3} + \sqrt {x} \]

[In]

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

[Out]

4*x**(3/2)/3 + sqrt(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {4}{3} \, x^{\frac {3}{2}} + \sqrt {x} \]

[In]

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

[Out]

4/3*x^(3/2) + sqrt(x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {4}{3} \, x^{\frac {3}{2}} + \sqrt {x} \]

[In]

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

[Out]

4/3*x^(3/2) + sqrt(x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \left (\frac {1}{2 \sqrt {x}}+2 \sqrt {x}\right ) \, dx=\frac {\sqrt {x}\,\left (4\,x+3\right )}{3} \]

[In]

int(1/(2*x^(1/2)) + 2*x^(1/2),x)

[Out]

(x^(1/2)*(4*x + 3))/3