3.2247 \(\int \frac{\left (1+\sqrt{x}\right )^3}{\sqrt{x}} \, dx\)

Optimal. Leaf size=13 \[ \frac{1}{2} \left (\sqrt{x}+1\right )^4 \]

[Out]

(1 + Sqrt[x])^4/2

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Rubi [A]  time = 0.0101607, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{1}{2} \left (\sqrt{x}+1\right )^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 + Sqrt[x])^3/Sqrt[x],x]

[Out]

(1 + Sqrt[x])^4/2

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Rubi in Sympy [A]  time = 1.66345, size = 8, normalized size = 0.62 \[ \frac{\left (\sqrt{x} + 1\right )^{4}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1+x**(1/2))**3/x**(1/2),x)

[Out]

(sqrt(x) + 1)**4/2

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Mathematica [A]  time = 0.0068166, size = 25, normalized size = 1.92 \[ 2 x^{3/2}+\frac{x^2}{2}+3 x+2 \sqrt{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + Sqrt[x])^3/Sqrt[x],x]

[Out]

2*Sqrt[x] + 3*x + 2*x^(3/2) + x^2/2

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Maple [B]  time = 0.002, size = 20, normalized size = 1.5 \[{\frac{{x}^{2}}{2}}+2\,{x}^{3/2}+3\,x+2\,\sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+x^(1/2))^3/x^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.4351, size = 12, normalized size = 0.92 \[ \frac{1}{2} \,{\left (\sqrt{x} + 1\right )}^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)^3/sqrt(x),x, algorithm="maxima")

[Out]

1/2*(sqrt(x) + 1)^4

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Fricas [A]  time = 0.236769, size = 23, normalized size = 1.77 \[ \frac{1}{2} \, x^{2} + 2 \,{\left (x + 1\right )} \sqrt{x} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)^3/sqrt(x),x, algorithm="fricas")

[Out]

1/2*x^2 + 2*(x + 1)*sqrt(x) + 3*x

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Sympy [A]  time = 0.445511, size = 20, normalized size = 1.54 \[ 2 x^{\frac{3}{2}} + 2 \sqrt{x} + \frac{x^{2}}{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1+x**(1/2))**3/x**(1/2),x)

[Out]

2*x**(3/2) + 2*sqrt(x) + x**2/2 + 3*x

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GIAC/XCAS [A]  time = 0.242263, size = 26, normalized size = 2. \[ \frac{1}{2} \, x^{2} + 2 \, x^{\frac{3}{2}} + 3 \, x + 2 \, \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)^3/sqrt(x),x, algorithm="giac")

[Out]

1/2*x^2 + 2*x^(3/2) + 3*x + 2*sqrt(x)